Can someone go over my work for this derivative?

[1MileCrash]

Homework Statement

Find dy/dx:

(3x^2+5x-2)^{sinx}

The Attempt at a Solution

y = (3x^2+5x-2)^{sinx}

ln y = ln [(3x^2+5x-2)^{sinx}]

ln y = sinx [ln(3x^2+5x-2)]

\frac{1}{y} \frac{dy}{dx} = cosx[ln(3x^2+5x-2)] + sinx[\frac{6x+5}{3x^2+5x-2}]

\frac{dy}{dx} = [3x^2+5x-2]^{sinx} [ cosx[ln(3x^2+5x-2)] + sinx[\frac{6x+5}{3x^2+5x-2}] ]

 

[tmiddlet]

That looks good to me.

 

[Precursor]

Looks fine.

If you simply want to check whether you're differentiating correctly, you could double check with wolfram alpha http://www.wolframalpha.com/input/?i=differentiate+y=[(3x^2++5x+-2)^(sinx)]".

It actually does a lot more than that, so it's a pretty useful tool.

 

[1MileCrash]

Thanks fellas.