Simplifying differential solutions - cotx e^4x

Question is f(x) = e^4x cotx

Fine, I'll use product rule;

dy/dx = V du/dx * U dv/dx

Let U = e^4x du/dx = 4e^4x

V = cot x dv/dx = -cose^2 x

so dy/dx = cotx 4e^4x + e^4x (-cosec x)

Now to simplifying;

dy/dx = e^4x(4 cot x - cosec^2 x)

Hmmm! I'm sure there's more to it. Can anyone help please.

Re: Simplifying differential solutions - cotx e^4x

Quote:

Originally Posted by

**froodles01** Question is f(x) = e^4x cotx

Fine, I'll use product rule;

dy/dx = V du/dx * U dv/dx

Let U = e^4x du/dx = 4e^4x

V = cot x dv/dx = -cose^2 x

You mean "-cosec^2 x" but that is obviously a typo.

Quote:

so dy/dx = cotx 4e^4x + e^4x (-cosec x)

Now to simplifying;

dy/dx = e^4x(4 cot x - cosec^2 x)

Hmmm! I'm sure there's more to it. Can anyone help please.

What you have is correct. Nothing more to it!