Derivative of cos(x)^(x+7)

Help! I haven't the slightest clue on how to do this...

thanks in advance!

Answers and Replies

Help! I haven't the slightest clue on how to do this...

thanks in advance!

$$y=cos^{x+7}(x)$$

Start by taking the natural logarithmic of both sides.

even the y?

so i'd have:

ln(y) = (x+7)ln(cos(x))

how do i get rid of the ln on the y?

cause i knew it was a ln problem, just i dont know how to get rid of the ln on the y

Don't worry about 'getting rid of the ln' yet. The problem is about taking derivatives, so take one and see what happens.

Mark44
Mentor
If you take the derivative of the left side, you should get (1/y)(dy/dx). On the right side, you should have the derivative of ((x + 7)ln(cos x)). Solve the resulting equation for dy/dx.