What is the derivative of a constant times a trig function?

Question

Such as f(x)= C sin(x);

ie f(x) = 3 sin (x)... what is f ' (x)?

Answer 1

3 cos x

Constant stays and differentiate the sin x!  

Answer 2

3 cos x

Just keep the constant and multiply by the deriv. of the trig function.

Answer 3

Hi,

For this question, always remember that it's legal to factor out the constant if it bothers you, so you can get:

3 dy/dx [ sin ( x ) ]

Now, we know the derivative of sin(x) is cos(x) so let's apply that knowledge to get:

3cos(x) = y' <=== FINAL ANSWER

I hope that helps you out!  Please let me know if you have any other questions!