Find the derivative of the function:

Question

f(x)=(4-e^-3x)^3? 

Answer 1

The function f(x) = (4 - e^-3x)³

Differentiate with respect to x.

Apply chain rule in derivatives.

Apply the formula d/dx(e^x) = e^x

d/dx(xⁿ) = nx^n-1

d/dx(x) = 1

d/dx(constant) = 0

f'(x) = 3(4 - e^-3x)² (d/dx)(4 - e^-3x)

= 3(4 - e^-3x)² (3e^-3x)

= 9e^-3x[(4 - (1/e^3x)]²

= 9(1/e^3x)[(4e^3x - 1)/e^3x)]²

= 9(1/e^3xe^6x)(4e^3x - 1)²

= 9(1/e^9x)(4e^3x - 1)²

f'(x) = 9e^-9x(4e^3x - 1)².