# Find the derivative of the following functions $$\displaystyle{y}={10}^{{{\ln{{2}}}{x}}}$$

Find the derivative of the following functions
$y={10}^{\mathrm{ln}2x}$
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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: $\frac{{10}^{\mathrm{ln}\left(2x\right)}\mathrm{ln}\left(10\right)}{x}$