find derivative of: (3x^2-1x+7)^cos(x)?

Answer 1

There are two standard techniques for finding the derivative of a function of the form
f(x)^g(x).

1) logarithmic differentiation.

Let y = f(x)^g(x). then take the natural log of both sides.

ln y = ln [ f(x)^g(x)] .

Now use the log property ln a^b = b lna, to get

ln y =g(x) ln f(x)

Now differentiate implicitly. On the left you will get (1/y) y', and on the right you will use the product rule and chain rule. Then multiply both sides by y, and you will have solved for y'.


2) or, you can use the fact that a=e^lna, to observe

f(x)^g(x) = e^ln[f(x)^g(x)]= e^[ g(x) lnf(x)], and then go to town with differentiation rules.

Answer 2

6x-1^ -sinx