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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