Question

If f(x)=5cos(2ln(x)), find f'(x).

My answer is (-5sinx)(2lnx)+(5cosx)(1/x)

I just did the product rule

can you verify if this is correct please!
no, I think MathMate did the same question a bit back but I can't find it.

You don't have a product
think of (2lnx) as the "angle"

how about letting p = 2lnx

then y = 5cos(p)
and dy/dx = -5sin(p)dp/dx

but dp/dx = 2/x

so dy/dx = -5sin(p)(2/x)
= -5sin(2lnx)(2/x)
= (-10/x)(sin(2lnx))

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