2ae2x 2ae2x. Let a be a real valued constant. Find the derivative with respect to x: y = -1 4xe2x O y (x) = (2ae2x – 1)² -8ae2x O y (x) = (2ae2x – 1) O y (x) = -4ae2x (2ae2x – 1)° 2ae2x O y (x) = (2ae2x – 1)

Q: nd the derivative of the function y(x) = c² + x°. Assume that c is a positive constant. (z) =

A: We have to find

Q: (a) f(x) = Vx(x² + x – 4)

A: the given function is: f(x)=x3x2+x-4

Q: Find the derivative of y with respect to x. y = cos1 (5x2 + 4) 10x + (5x2 + 4)2 -10x Vi- (5x2 + 4)?…

A: The given function is  y= cos-1(5x2+4)  We have to find the derivative of this function w.r.t. x

Q: Find the derivative. g(x) = (4x – 2)° – Vr + 8

A:

Q: Find the derivatives – do not simplify a. y= x4- 3square root of x + 5x2/3 +8/x-3

A: ddxxn=n xn-1

Q: Find the derivative of the function. 4² – 1 4x 4x g(x) = du Hint: f(u) du = f(u) du + f(u) du Jax u…

A:

Q: (b) g(x) = (1+4x)*(3+ x – x²)®

A: ddxuv=vdudx+udvdxHere u= 1+4x5, v=3+x-x28dudx=51+4x4×4  ,   dvdx=83+x-x27×-3x2g'x=3+x-x28  5 1+4x4 4…

Q: 2. Find the derivatives: (a) f(x)=(x² - 2x+1) (x² -1) x+2x+5 (b) f(x): %3D x² +1

A: Part (a) Given a function Using product rule of the derivative