Find the derivative of fx sinxcosx using the product ruleSo

Find the derivative of f(x) = sinx*cosx using the product rule

Solution

Given f(x) = sinx*cosx

We need to find f\'(x) using the product rule.

Then we will assume that f(x) = u*v such that:

u= sinx ==> u\' = cosx

v= cosx ==> v\' = -sinx

Then we know that:

f\'(x) = u\'v + uv\'

==> f\'(x)= cos^2 x - sin^2x

But we know that cos2x = cos^2x - sin^2 x

==> f\'(x) = cos^2 x - sin^2 x = cos2x