How do you differentiate f(x)=ln2x * sin4x using the product rule?

1 Answer
Pietro P.
Jun 1, 2016

f'(x)=(2sin(4x))/2x + 4cos(4x)ln2x

Explanation:

The product rule says you take the derivative of your first function and multiply it by the second and add it to the product of the derivative of your second function and your original first function.

We start with taking the first derivative of function ln2x, which is 2/2x(don't forget to chain rule). we then multiply this by our second function, sin(4x), which results in the first piece 2sin(2x)/2x.

We then take the derivative of our second function, sin(4x), which is 4cos(4x)(again don't forget to chain rule). Then multiply this by the first function to get 4cos(4x)ln2x.

Lastly add them up to get the final answer f'(x)= (2sin(4x))/2x + 4cos(4x)ln2x. Hope this helped.

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