Find the derivative of the following functions

$y={10}^{\mathrm{ln}2x}$

Samara Richard
2022-03-22
Answered

Find the derivative of the following functions

$y={10}^{\mathrm{ln}2x}$

You can still ask an expert for help

Regan Gallegos

Answered 2022-03-23
Author has **9** answers

Step 1

We use the chain rule

$y={10}^{\mathrm{ln}\left(2x\right)}$

$\frac{dy}{dx}={10}^{\mathrm{ln}\left(2x\right)}\mathrm{ln}\left(10\right)\frac{d}{dx}\mathrm{ln}\left(2x\right)$

Step 2

We again use the chain rule

$\frac{dy}{dx}={10}^{\mathrm{ln}\left(2x\right)}\mathrm{ln}\left(10\right)\frac{1}{2x}\frac{d}{dx}\left(2x\right)$

$\frac{dy}{dx}={10}^{\mathrm{ln}\left(2x\right)}\mathrm{ln}\left(10\right)\frac{1}{2x}\left(2\right)$

$\frac{dy}{dx}={10}^{\mathrm{ln}\left(2x\right)}\mathrm{ln}\left(10\right)\frac{1}{x}$

$\frac{dy}{dx}=\frac{{10}^{\mathrm{ln}\left(2x\right)}\mathrm{ln}\left(10\right)}{x}$

Answer:$\frac{{10}^{\mathrm{ln}\left(2x\right)}\mathrm{ln}\left(10\right)}{x}$

We use the chain rule

Step 2

We again use the chain rule

Answer:

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