Thread: 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)


I appreciate your help

Thanks

The first one is fine.

Question b) provided the bracket you missed is at the beginning of the function and it is your answer is correct but I think you made a typo at the end where it should have you missed the .

The third one is also fine.

I understand it can be confusing when using the chain rule and you can doubt yourself whether you've done it right but you managed it all well by yourself.