Derivative Help!?

Question

1.) Find f'(x) for f(x) = 8e^x + 4 ln (x^3)


2.) Find f'(x) for f(x) = 6e^5x + 8 ln(8x + 1)

I'm stuck on how to do find the derivatives of these two questions, any help would be appreciated!!

Answer 1

1) f(x) = 8e^x + 4 ln (x^3)
f'(x) = 8e^x + 4(3x²)(1/x^3)
f'(x) = 8e^x + 12x²/x^3
f'(x) = 8e^x + 12/x

2) f(x) = 6e^5x + 8 ln(8x + 1)
f'(x) = 6(5)e^5x + 8(8)[1/(8x+1)]
f'(x) = 30e^5x + 64/(8x+1)

Answer 2

Part a - First use definition of the ln function ln(x^n) = n*ln(x) so you get

f(x) = 8e^x +4*3*ln(x) = 8e^x+12 ln(x)

Then f'(x) = 8e^x +12/x

Part b. Use d e^(ax)/dx =a*e^(ax) and d ln(nx+b)/dx = n/(nx+b) (use chain rule) then

f'(x) = 6*5*e^5x +8*8/(8x+1) = 30 e^5x +64/(8x+1)

Answer 3

1) f'(x)=8e^x + (4 / x^3)3x^2
=8e^x +12 x^2/x^3
=8e^x+12/x

2)f'(x)=6e^5x(5) + (8 / (8x+1))8
=30e^5x +64 / (8x+1)