Here is what you get as an answer usually when you ask a question on Calculus or even Physics in my experience and evidently the asker was satisfied. The person answering is a professor at a college. This girl asked on line for help on what the derivative of 4cos(5x2) was. This is a chain rule problem. How would you like it answered?

Best answer as selected by question asker.
For a function f(x) = g(h(x)), express h(x) as y.
Then f(x) = g(y), f’(x) = [d {g(y)}/ dy]*(dy/dx).
Here we have to find the derivative of f(x)= 4 cos (5x2).
Let y=5x2, this gives f(x)= 4 cos y
f’(x)= [d (4 cos y)/dy]*[d(5x2)/dx]
We also know that the derivative of cos x= sin x.
=> [d (4 cos y)/dy]= 4 sin y
[d(5x2)/dx]= 5
Therefore f’(x)= [d (4 cos y)/dy]*[d(5x2)/dx]
= (4 sin y)*5
=4*sin (5x2)*5
=20 sin (5x2)
Therefore the derivative of 4 cos (5x2) is 20 sin (5x2)