Find the following derivatives by using Chain Rule. a) dz/dt, where z = x sin y, x = t², and y = 4t³ [Ans: 2t sin 4t³ + 12t4 cos 4t³] b) dw/dt, where w = cos 2x sin 3y, x = t/2, and y = t*. [Ans: – sin t sin 3t* + 12t3 cos t cos 3t4] c) dw/dt, where w = xy sin z, x = t², y = 4t³, and z = t + 1. %3D [Ans: 20t4 sin(t + 1) + 4t5 cos(t + 1)] d) dU/dt, where U = In(x + y + z), x = t, y = t², and z = t³. %3D 1+2t+3t². [Ans: t+t2+t3

Q: g. y = ex² +1 h. y = esinx y = ln(sin x) i. j. y = ln² + e√x X 6. L

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Q: Find the following derivatives: 1) y = sincos2x?

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 6. Use implicit differentiation to find the following derivatives for the equation tan y = 4 +x?y +…

A: see below the calculation and answer

Q: Find the derivative of y = In O O a.) dy dx =In(5) +4ln(x) —In(cosx) 4 1 dx X COSX b.) dy = c.) dy 1…

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Q: Find the derivative of y with respect to s. y= sec 1(7s° + 4)

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Q: Find the derivatives of each of the following functions f(x)=-2 sinx b) y=-cos²x c) y = 3x sin x d)…

A: find the dervative

Q: 2.) Compute for the derivative (DO NOT USE THE DEFINITION) of A. 2x3 y = tanh sin x2

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Q: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: X.

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Q: Find the indicated derivative dy/dx 3.) x+xy+y=1

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: 1. Find each derivative. a) y = sin- X c) f(x) = ln- sin x COS X b) y = cos(x² - 2x-8)

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Q: Find the derivative of 7 (t) = (1+t°, te¯t, sin (2t)) A. F'(t) = (3t°, (1 + t)e¯t, 2 cos (2t)) B.…

A: We are asked to find the derivatives.