Homework Help: Can someone go over my work for this derivative?

1. Jul 23, 2011

1MileCrash

1. The problem statement, all variables and given/known data

Find dy/dx:

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

3. The attempt at a solution

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

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

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

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

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

2. Jul 23, 2011

tmiddlet

That looks good to me.

3. Jul 23, 2011

Precursor

Last edited by a moderator: Apr 26, 2017
4. Jul 23, 2011

1MileCrash

Thanks fellas.