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.

Quote:

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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

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

Quote:

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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.

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What you have is correct. Nothing more to it!