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(5x-2) was. This is a chain rule problem. How would you like it answered?
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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 (5x-2).
Let y=5x-2, this gives f(x)= 4 cos y
f’(x)= [d (4 cos y)/dy]*[d(5x-2)/dx]
We also know that the derivative of cos x= -sin x.
=> [d (4 cos y)/dy]= -4 sin y
[d(5x-2)/dx]= 5
Therefore f’(x)= [d (4 cos y)/dy]*[d(5x-2)/dx]
= (-4 sin y)*5
=-4*sin (5x-2)*5
=-20 sin (5x-2)
Therefore the derivative of 4 cos (5x-2) is -20 sin (5x-2)