# Derivatives - using differentiation rules

• February 17th 2009, 03:54 PM
calcbeg
Derivatives - using differentiation rules
Hi can some more knowledgeable than I please check my work?

Calculate the derivative using the differentation rules

a)

f(x) = (4x^4 - (2/5)x^3)^1/4

f'(x) = 1/4 (4x^4 -2/5x^3)^-3/4 (16x3-(6/5)x^2)

b)

f(x) = e^-5x + 3tan4x)^5

f'(x) = 5(e^-5x+3tan4x)4(-5e^-5x+12sec^2)

c)

f(x) = √(cosx + √x^7)

f'(x) = 1/2 (cosx + x^7/2)^-1/2 (-sin + (7/2)x^5/2)

Question b) provided the bracket you missed is at the beginning of the function and it is $f(x) = (e^{-5x} + 3\tan 4x)^5$ your answer is correct but I think you made a typo at the end where it should have $12\sec^2 4x$ you missed the $4x$.