# Homework Help: Easy Derivative - Not easy for me, though!

1. Nov 18, 2007

### fiziksfun

1. Derivate x^(2sinx)

3. I used implicit differentiation because there's an x in the base and in the exponent.
I have all of my work in the picture (if you cant see it in the attachment):

http://i12.tinypic.com/7x1sn44.jpg

I don't get the same answer as the correct answer which is 2cosx(x^2sinx), and I can't figure out why!!

Am I doing something wrong, or is it possible the answer is wrong !?

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2. Nov 18, 2007

### Moridin

Try substituting t = 2 sin x and you will get x^t where t(x). Differentiate x^t. What are you going to do if you get any t':s in your equation?

3. Nov 18, 2007

### rocomath

i'm getting the same answer as you

4. Nov 18, 2007

### fiziksfun

ya i just i checked my answer using a graph - its right and the other answer is wrong - thanks!

5. Nov 18, 2007

### rocomath

anytime :-]

6. Nov 18, 2007

### dynamicsolo

Whoever provided the 'correct' answer just treated it like d/dx (a^u), which only works for a constant a > 0. When the base of the exponential function is itself a variable or function, logarithmic differentiation is called for, which is what you did. (I sure hope that wasn't a TA or instructor who wrote that 'answer'...)