how to find a derivative with just variables and when an exponent is raised to another exponent. (correct me please)

Question

so the question states h(y)= (b/a+y^3)^5

I am not sure how to do this with just variables but I assumed a and b to be constants since they aren't variables from the equation. I then found this derivative

5(b/a+y^3)^4 * (-3y^2 /(a+y^3)^2)

using the chain rule but I got it wrong. I was wondering if you could help me fix my mistakes.

The second portion of this assignment section was P(t)= 6*e^(-2e)^(2t).

I was very confused because the power is raised to another power. so I tried combining the chain rule with the product rule. I got   -6*(e^(-2e)^(2t) * -2e^2t)

but I got this derivative wrong. Please help me figure out where I went wrong.

Answer 1

It looks like you left out b in the numerator when doing the quotient rule in the first part.

 

For the second portion, notice you have e^f(t), where f(t) = -2e^2t. Then note f'(t) = -4e^2t, and

 

d/dt 6*e^(-2e^2t) = 6 d/dt e^f(t) 

 

= 6 f'(t)e^f(t)

= -24e^2te^(-2e^2t).