Hi

I would appreciate if someone could check my work.

Differentiate the following functions

a)

f(x) = ln (tan 3x + cos 5x)^2

f'(x) = (1/(tan 3x + cos 5x)^2) (2(sec^2^x + -sin 5x))

f'(x) = (2sec^2 3x - 2sin 5x)/((tan 3x + cos 5x)^2)

b)

f(x) = e^x^3 + 2ln x) cos (1/x^2))

f'(x) = (e^x^3 + 2 ln x) ((-sin (1/x^2))(-2x)) + (e^x^3 + 2/x) (cos (1/x^2))

c)

f(x) = sin ^ tan x

ln f(x) = ln (sin ^ tanx)

ln f(x) = tanx (ln sin)

f'(x) (1/f(x)) = ((sec^2 x) (ln sin) + (1/sin)(tanx))

f'(x) = sin ^tan x ((sec^2x)(ln sin) + (1/sin)(tan x))

Thanks in advance