Derivatives??

Question

Find h'(y) if h(y)=tan(e^(3y))


Ok, so i used the product rule, but i'm not sure if i'm suppose to..

This is what i got
f= tan(e^3y) g=e^3y

so i got
3e^3y*tan(e^3y) + sec^2(e^3y) * e^3y


is it correct?? if not, can u show me how please?

Answer 1

you use the chain rule

h(y) = tan(e^(3y))

u=e^(3y)
u'=3e^(3y)

h(u) = tan(u)
h'(u) = sec^2(u)

h'(y) = h'(u)*u'

h'(y) = 3e^(3y)*sec^2(e^(3y))

excuse my notation if it is wrong, I'm used to writing everything like dy/dx.

Answer 2

Calculate the derivative.
h(y) = tan(e^(3y))

You want to use the chain rule since it is nested functions.

h'(y) = sec²(e^(3y)) [3e^(3y)]

h'(y) = 3e^(3y) * sec²(e^(3y))

Answer 3

if you use the chain rule, there shouldn't be any adding in the middle/=