Y=(x1)(x2)/x^1/2 = (x^23x2)/x^1/2 dy/dx=√x(2x3)1/2√x(x^23x2)/(√x)^2 dy/dx =2x(2x3)(x^23x2)/2x√xx dy/dx =4x^2–6xx^23x2/2x√x dy/dxQ If y = 2^x, find dy/dx ANSWER 1) Take Logs of both sides of our equation y = 2^x So we get log (y)=log (2^x) 2) Apply relevant log rule to rhs Log rule log (a^b) = b log (a) nb the dot between b and log (a) represents x / multiply / times ) So we get log (y) = x log (2) Transcript Ex 96, 3 For each of the differential equation given in Exercises 1 to 12, find the general solution = 2 = 2 Differential equation is of the form = where P = 1 and Q = x2 Finding integrating factor, IF = e IF = e 1 IF = e log IF = x Solution is y (IF) = yx = 2
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Find (dy)/(dx) if y=sin(tan^(-1)(x^(2)))-Solve the differential equation dy/dx = y/x Solve the differential equation dy/dx = y/xThis is the Solution of Question From RD SHARMA book of CLASS 12 CHAPTER DIFFERENTIAL EQUATIONS This Question is also available in R S AGGARWAL book of CLASS
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Ex 94, 12 Find a particular solution satisfying the given condition 𝑥 𝑥2−1 𝑑𝑦𝑑𝑥=1;𝑦=0 When 𝑥=2 𝑥 𝑥2−1 dy = dx dy = 𝑑𝑥𝑥(𝑥2 − 1) Integrating both sides 𝑑𝑦 = 𝑑𝑥𝑥(𝑥2 − 1) 𝑦 = 𝑑𝑥𝑥(𝑥 1)(𝑥 − 1) We can write integrand as 1𝑥(𝑥 1Since 2 2 is constant with respect to x x, the derivative of 2 2 with respect to x x is 0 0 2 x 0 2 x 0 Add 2 x 2 x and 0 0 2 x 2 x 2x 2 x Reform the equation by setting the left side equal to the right side y' = 2x y ′ = 2 x Replace y' y ′ with dy dx d y d x dy dx = 2x d y d x = 2 x 862 views around the world You can reuse this answer Creative Commons License
Watch Video in App This browser does not support the video element 327 k 16 k Answer Step by step solution by experts to help you in doubt clearance & scoring excellent{eq}y\sin(x^2y^2)=xy1 {/eq} Implicit Differentiation Implicit differentiation is a name given to the process of differentiating an implicit function, but what it really is is yet another dy/dx = (((x 1)(x 2))/sqrt(x))(1/(x 1) 1/(x 2) 1/(2x)) I'm assuming the function is y = ((x 1)(x 2))/sqrt(x) I will use logarithmic differentiation to compute this derivative
If y = √(sin x y), then dy/dx equals A(cos x)/(2y 1) B (cos x)/(1 2y) C (sin x)/(1 2y) D (sin x)/(2y 1)D dx (y2) = d dx (1 1−x2) d d x (y 2) = d d x (1 1 x 2) Differentiate the left side of the equation Tap for more steps 2y d dx y 2 y d d x y Ex 55, 12 Find 𝑑𝑦/𝑑𝑥 of the functions in, 𝑥^𝑦 𝑦^𝑥 = 1 𝑥^𝑦 𝑦^𝑥 = 1 Let 𝑢 = 𝑥^𝑦 , 𝑣 = 𝑦^𝑥 Hence, 𝑢𝑣=1 Differentiating both sides 𝑤𝑟𝑡𝑥 (𝑑(𝑣〖 𝑢〗))/𝑑𝑥 = 𝑑(1)/𝑑𝑥 𝑑𝑣/𝑑𝑥 𝑑𝑢/𝑑𝑥 = 0 (Derivative of
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Find Dy/dx Y = Integral^x_0 Squareroot 1 T^2 Dt Y = Integral^0_Squareroot X Sin (t^2) Dt Y = Integral^x_1 T^2/t^2 4 Dt Integral^x_3 T^2/t^2 4 Dt Y = (integral^x_0 (t^3 1)^10 Dt)^3 Y = Integral^sin X_0 Dt/Squareroot 1 T^2, x < Pi/2 If y = sin^1 (x√(1 x) √x √(1 x^2) and dy/dx = 1/2 √x√(1x^2) p, then p is equal to askedin Mathematicsby ShivamK(681kpoints) jee jee mains 0votes 1answer The degree of the differential equation satisfying √(1 x^2) √(1 y^2) = kx√(1 y^2) – y√(1 x^2Find dy/dx y=1/ (x^2) y = 1 x2 y = 1 x 2 Differentiate both sides of the equation d dx (y) = d dx ( 1 x2) d d x ( y) = d d x ( 1 x 2) The derivative of y y with respect to x x is y' y ′ y' y ′ Differentiate the right side of the equation Tap for more steps Apply basic rules of exponents
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DIFFERENTIATE ON BOTH SIDE'S WRT x WE HAVE (1/2) x½¹ (1/2) y½¹ × dy/dx = 0 x½ y½ dy/dx = 0 y½ × dy/dx =x½ y½ dy/dx =1/√x dy/dx =(1/√x) × y½ dy/dx =√y/√xAnswer to Find the differential dy y = 1/x 2 dy = (b) Evaluate dy for the given values of x and dx x = 0 and dx = 001 dy =Solution Solution y = sin − 1 (1 x 2 2 x ) ⇒ sin y = 1 x 2 2 x ⇒ cos y = 1 − sin 2 y = 1 − (1 x 2 2 x ) 2 = 1 x 2 1 − x 2 Differentiating it wrt x, cos y d x d y = (1 x 2) 2 2 (1 x 2) − 2 x (2 x) ⇒ cos y d x d y = (1 x 2) 2 2 (1 − x 2) ⇒ d x d y = cos y 1 ((1 x 2) 2 2 (1 − x 2) ) ⇒ d x d y = 1 − x 2 1 x 2 ∗ ((1 x 2) 2 2 (1 − x 2) ) ⇒ d x d y = 1 x 2 2
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Dy dx = d dxlnx− d dxln(1x2) = 1 x − 1 1x2 ⋅ d dx (1x2) = 1 x − 1 1x2 ⋅2x = 1 x − 2x 1x2 d y d x = d d x ln x − d d x ln ( 1 x 2) = 1 x − 1 1 x 2 ⋅ d d x ( 1 Ex 53, 8 Find 𝑑𝑦/𝑑𝑥 in, sin2 𝑥 cos2 𝑦 = 1 sin2 𝑥 cos2 𝑦 = 1 Differentiating both sides 𝑤𝑟𝑡𝑥 (𝑑 (sin2 𝑥 cos2 𝑦))/𝑑𝑥 = (𝑑 (1))/𝑑𝑥 (𝑑 (sin2 𝑥))/𝑑𝑥 (𝑑 (cos2 𝑦))/𝑑𝑥 = 0 Calculating Derivative of sin2 𝑥 & cos^2 𝑦 sepretaly Finding Derivative of 𝒔𝒊𝒏𝟐 𝒙 (𝑑 (sin2Differentiate both sides of the equation d dx (y) = d dx ( x 1 x 2) d d x ( y) = d d x ( x 1 x 2) The derivative of y y with respect to x x is y' y ′ y' y ′ Differentiate the right side of the equation Tap for more steps
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views around the world You can reuse this answer Creative Commons License If x = cos t (3 2cos^2 t) and y = sin t (3 2sin^2 t), find dy/dx at t = pi/4 asked in Mathematics by Samantha ( 3k points) continuity and differntiability Misc 13 Find 𝑑𝑦/𝑑𝑥 , if 𝑦=〖𝑠𝑖𝑛〗^(−𝟏) 𝑥〖𝑠𝑖𝑛〗^(−1) √(1−𝑥2), – 1 ≤ 𝑥 ≤ 1 𝑦=〖𝑠𝑖𝑛〗^(−
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreVerify that x^2 cy^2 = 1 is an implicit solution to \frac {dy} {dx} = \frac {xy} {x^2 1} If you're assuming the solution is defined and differentiable for x=0, then one necessarily has y (0)=0 In this case, one can easily identify two trivial solutions, y=x and y=x If you're assuming the solution is defined and The nice thing about this differential equation is that the dy dx is already isolated, therefore the answer can be obtained by simply integrating both sides ∫dy = ∫3x 2 x2 dx y = 3 2x2 −2x−1 C y = 3 2x2 − 2 x C 2 = 3 2 (1)2 − 2 1 C 4 − 3 2 = C 5 2 = C
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreImage transcriptions From question given y= ely, we have to find the differential dy whenox = 2 andlax = 04 long (b) when * = 2 and dx = 005 0 since dy = leyda Now put x= 2 and dx= 04 in equation to findvalue ofdy we get, 16 dy Ley ( 0Calculus Find dy/dx y=x^2e^x y = x2ex y = x 2 e x Differentiate both sides of the equation d dx (y) = d dx (x2ex) d d x ( y) = d d x ( x 2 e x) The derivative of y y with respect to x x is y' y ′ y' y ′ Differentiate the right side of the equation Tap for more steps
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5) d dx x x x () 10 10 1 g32 g16 6) If y = log x then dy dx = 1 x 7) If y = e 2 then dy dx = 2e 8) The derivative of a x is a xloga 9) The derivative of x m y n = (xy) (mn) is x y QIV Solve the following 1) If y = (6 x 3 − 3 x 2 −9 x) 10, find dy dx 2) If y = 3 8 5 2 4 5 x x g14 g14 g11 g12, find dy dx 3) If y = log(log(logx)) 2Find $ \dfrac{dy}{dx} $ if $ y = 2u^2 3u $ and $ u = 4x 1 $ I am trying to use the chain rule on it $$ \dfrac{dy}{dx} = \dfrac{dy}{du} \dfrac{du}{dx} $$ My work so far $$ \dfrac{d}{du}(2u^23u) * \dfrac{d}{dx}(4x1) = (4u3)(4) $$ However I am not absolutely sure I am doing it right and I don't have the answer in my bookFind dy/dx y= (x^2)/ (3x1) y = x2 3x − 1 y = x 2 3 x 1 Differentiate both sides of the equation d dx (y) = d dx ( x2 3x−1) d d x ( y) = d d x ( x 2 3 x 1) The derivative of y y with respect to x x is y' y ′ y' y ′ Differentiate the right side of the equation Tap for more steps
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Q Please copy and paste the graphs into this file and provide a brief explanation of each You will receive points off if you simply copy and paste the outputs without a description 3) Creating a Dataset and Examining Basic Descriptive Statistics We will use the fictional data in the table below (see next page) Transcript Ex 53, 9 Find 𝑑𝑦/𝑑𝑥 in, y = sin^(−1) (2𝑥/( 1 2𝑥2 )) 𝑦 = sin^(−1) (2𝑥/( 1 2𝑥2 )) Putting x = tan θ 𝑦 = sin^(−1"Find "(dy)/(dx)" for "y=sin(x^(2)1) Updated On To keep watching this video solution for FREE, Download our App Join the 2 Crores Student community now!
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Y 1 d y = x − 1 d x Variable x cannot be equal to 1 since division by zero is not defined Multiply both sides of the equation by \left (x1\right)\left (y1\right), the least common multiple of y1,x1 Variable x cannot be equal to 1 since division by zero is not defined Given that dy/dx = 9y²– 4 and that y = 1 when x = 2 Find an equation expressing x in term of y Example 9 Find the general solution of the differential equation 𝑑𝑦/𝑑𝑥= (𝑥1)/ (2−𝑦) , (𝑦≠2) 𝑑𝑦/𝑑𝑥= (𝑥 1)/ (2 − 𝑦) , (𝑦≠2) (2 − y) dy = (x 1) dx Integrating both sides ∫1 〖 (2−𝑦)𝑑𝑦=〗 ∫1 (𝑥1)𝑑𝑥 2y − 𝑦^2/2 = 𝑥^2/2 x c 〖4𝑦 − 𝑦〗^2/2 = (𝑥
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To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW If y= 1/x then dy/dx is Ex 53, 11 Find 𝑑𝑦/𝑑𝑥 in, 𝑦 = cos–1 ((1− 𝑥^2)/( 1 𝑥2 )) , 0 < x < 1 𝑦 = cos–1 ((1− 𝑥^2)/( 1 𝑥2 )) Putting x = tan θ yFind dy/dx y^2=(x1)/(x1) Differentiate both sides of the equation Differentiate the left side of the equation Tap for more steps Differentiate using the chain rule, which states that is where and Tap for more steps To apply the Chain Rule, set as
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