# Math - Derivatives

posted by .

How would one take the derivative of "f(x)^[g(x)]? Is there a formula I can follow to differentiate functions like that?

• Math - Derivatives -

you will have to take the natural log of both sides.
I will illustrate with an example

e.g.

y = (x^2+1)^(2x+3)
ln y = ln ((x^2+1)^(2x+3))
ln y = (2x+3)(ln(x^2+1)

now differentiate, using the product rule on the right side.
(dy/dx)/y = (2x+3)(2x/(x^2+1)) + 2ln(x^2+1)
dy/dx = y((2x+3)(2x/(x^2+1)) + 2ln(x^2+1))
you could then replace y with its original value and simplify, but that would be a general method.

## Similar Questions

the derivative of 2x^e is zero right or no?
2. ### math

can some one please help me with the following questions as i don't understand them please (a) write down the derivative of each of the functions f(x)=E7x and g(x)=cos(2x) using the product rule differentiate the function k(x)=E7xcos(2x) …
3. ### CALC

I am sorry i still don't know how to start. and i am sorry for the problem earlier..it wasn't my fault :( Note that the way students like you are asked to solve this and similar problems is usually not the way people like me solve …
4. ### Math derivatives

What is the derivative of: a) cos(3x) b) π/x I did (a) just by following chain rule: -sin(3x)*3 so it's -3sin(3x) Is that correct?
5. ### math

I studied derivatives before, but kind of forgot them all, is there a website that gives me an overview of derivatives. What is first and second derivatives, how to find it, all the derivative rules and so on... thank you
6. ### Calculus

I finished this problem but I wanted some feedback because I don't know if it's entirely correct. Suppose that functions f and g and their derivatives with respect to x have the following values at x=2. f(x)=8 g(x)=2 f'(x)=1/3 g'(x)=-3 …
7. ### Calculus (Derivatives)

What is the derivative of the this functon?
8. ### calculus

Differentiate both sides of the double angle identify sin 2x= 2 sin x cos x to determine an identify for cos x. Find the first derivative, second derivative, third fourth, fifth, sixth, seventh and eighth derivative. Use the results …
9. ### Calculus

Hello, I really need help on these two homework problem. >< In problem #1, I believe it is related to the exponential functions and their derivatives section...in Calculus II?
10. ### Calculus

What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like?

More Similar Questions