# Use logarithmic differentiation to find dy/dx given y = (x + 1)^(2x).

## Question:

Use logarithmic differentiation to find {eq}\frac{\mathrm{d}y}{\mathrm{d}x} {/eq} given {eq}y = (x + 1)^{2x} {/eq}.

## Logarithmic Derivative.

When calculating the derivative of a high function to another, we make use of the well-known logarithmic derivative.

This process allows to obtain a general formula to calculate this derivative, that is:

{eq}y\left( x \right) = m{\left( x \right)^{n\left( x \right)}} \to y'\left( x \right) = y\left( x \right)\left[ {n'\left( x \right)\ln m\left( x \right) + n\left( x \right)\frac{{m'\left( x \right)}}{{m\left( x \right)}}} \right] {/eq}

Applying the formula of the logarithmic derivative:

{eq}y\left( x \right) = m{\left( x \right)^{n\left( x \right)}} \to y'\left( x \right) = y\left(...

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Logarithmic Properties

from Math 101: College Algebra

Chapter 10 / Lesson 5
30K