Can someone go over my work for this derivative?

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    Derivative Work
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Homework Help Overview

The problem involves finding the derivative of the function \( y = (3x^2 + 5x - 2)^{\sin x} \), which falls under the subject area of calculus, specifically differentiation techniques involving logarithmic differentiation.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply logarithmic differentiation to simplify the process of finding the derivative. Some participants affirm the correctness of the approach without delving into specific details.

Discussion Status

The discussion appears to be supportive, with participants confirming the original poster's work. There is mention of using an external tool for verification, indicating a productive direction in checking the differentiation process.

Contextual Notes

No explicit constraints or missing information are noted, but the use of an external tool for verification suggests a reliance on additional resources for confirmation of the work presented.

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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}] ]
 
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That looks good to me.
 
Thanks fellas.
 

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