Find y' at the specified point. x² + y? = 81, at (0, – 9) y'

Q: Find the derivative dydx for the function x=sin2t, y=−cost at the point t=π6.

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Q: first derivative y= 4in Gty) is dy 4.

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Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

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Q: Find the equation of tangent and equation of normal for the implicit function y + 4xy x+y, at the…

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Q: Calculate the derivative. y = tanh(t2 + 1)

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Q: and dr= %3D Solve for the differential of y When y=sinxx x

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Q: Find the derivative of the function y = sech−1 (sin x), 0 < x <   /2

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Q: Find y" by implicit differentiation Va + Vy= 4

A: To  Determine: find the implicit differentiation Given: we have x+y=4 Explanation: we have x+y=4 so…

Q: Solve for the differential of y when y=sinzx, x=-, and dx=- 3 2

A: Pi/4

Q: Use differential to approximate the change in y=x3+x2 as x changes from 1 to 0,95.

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Q: Use differentials to approximate the quantity   √17

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Q: Find the differential of the function y = x- sin x.

A: Given: y=x2-sinx

Q: 5. Second derivative of y = 1+t)< t2

A: Given: y = 1+t2t2 To find: Second derivative of the given function.

Q: calculate the derivative. y = tanh(t2 + 1)

A: Given: calculate the derivative.  y = tanh(t2 + 1)

Q: X 1.-+ J y = 37ab2, y" X

A: Let's find.

Q: ,2x Calculate the second derivatives of function f(x) = sin(x) + Ide²x at point x = 0.625 using…

A: Three point central differential formula for 2nd derivative   f′′(x)= f(x-h)-2f(x)+f(x+h)h2 Five…

Q: dy by implicit differentiation: 2x 3x? y + y = 15 Find - dx

A: Take the derivative by concept of power derivative and chain rule of derivative.

Q: Find the derivative of the function. y = ek tan(V 5x) y'(x)

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Q: 13. Find the second derivative y “ of y = 5z2 +sinrcosz

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Q: use differentials to approximate the change in y if x changes from 25 to 25.3

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Q: Use central difference approximations to estimate the first and second derivatives of y = e* at x =…

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Q: Find the derivative of the function g(x)= integral  x2  tanx  (1/square root 4+t4) dt

A: Leibnitz integral rule for Differentiation :               ddx ∫α(x)β(x) f(t,x) dt = ∫α(x)β(x)…

Q: Find the partial derivative. = sin (10x*y+ 11xy) dz dx

A: Given function:-    z = sin(10x3y + 11xy2)

Q: Solve for the differential of y when y=sinxx• x=-. and dx= 3 4 2

A: i am going to solve the given problem by using some simple calculus to get the required result.

Q: Solve for the differential of y when y= sinzx. x= -, and dx 3 2 4

A: we have to solve the problem

Q: Find the derivative of the function. y = tanh-(6x) V6 1+ 6x y' =

A: derivative of the function..

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: Find the equation of tangent and equation of normal for the implicit function y +3xy =x+y, at the…

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Q: Find the derivative of the function. y = 13 arctan V (v²) y' =

A: We have to find the derivative of the function  y = 13 arctanx.

Q: i) S'(2x – 1)* dx (In x)2 j) fth dx 7 k) S (1-- -)dx (x2+1) 1) S(1+ tan² x) dx

A: I am attaching image so that you understand each and every step.

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: 6) Calculate - dx for z = ln(x + y²).

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Q: Find the differential of the function. y = 1 divided by x^7 - 8x dy =

A: we have to find dy

Q: The average rate of change of the function y = sinx over the interval [0, ]is 4

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Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

Q: dy Exc:" of y = tanh (x5 – 5x)² --

A: Solution:Given         y=tanh4(x5-5x)2  To find dydxFormula:ddx(xn)=nxn-1ddx(tanh x)=sech2x

Q: Find the second derivative y “ of " of y = 5z +sin zcosz

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Q: Find the differential for y = tan 2x2

A: Find the differential equation for given equation We need to take derivative for tan using the…

Q: n. y= (x+Inx)

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Q: Solve for the differential of y when y=sinxx: x=-, and dx 3 2 2 2 4

A: y=sinπx, x=13, dx=12

Q: Find the equation of the tangent line to the curve y = ln(4 ln x) at the point where x = e. %3D

A: It can be solved using differentiation.

Q: 7) y=cos/2x+1

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Q: The derivative of y=eSinh/x +cosh¬/x equals

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Q: Find dy/dx by implicit differentiation   4Sin (x2) =x Sin (y2)

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Q: 2 S Sec'x In cotx) dx (

A: We will solve the problem.

Q: 12. y= tanh(t2 +1)

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Q: -Find for: y= sinV1-t dx

A: We have to find dydx for y=sin-11-x4.

Q: 1 dy if y = dx -1 Find - tan 3x. dy dax

A: Use derivative formula

Q: calculate the derivative y = (sinh−1(x2))3

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…