Pam Stokes

2022-01-02

What is the derivative of ${10}^{x}?$

Jeremy Merritt

Beginner2022-01-03Added 31 answers

There is a rule for differentiating these functions

$\frac{d}{dx}\left[{a}^{u}\right]=\left(\mathrm{ln}a\right)\cdot \left({a}^{u}\right)\cdot \frac{du}{dx}$

Notice that for our problem a=10 and u=x so lets

Notice that for our problem a=10 and u=x so lets

Stella Calderon

Beginner2022-01-04Added 35 answers

Taking natural log on both sides,

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

We have,$\mathrm{ln}\left({a}^{b}\right)=b\mathrm{ln}a$

Likewise,$\mathrm{ln}\left({10}^{x}\right)=x\mathrm{ln}10$

So,$\mathrm{ln}y=x\mathrm{ln}10$

Now differentiate with respect to$x$

$\frac{1}{y}\cdot \frac{dy}{dx}=\mathrm{ln}10$

$\frac{dy}{dx}=y\mathrm{ln}10$

Plug in$y={10}^{x}$

$\frac{dy}{dx}={10}^{x}\mathrm{ln}10$

We have,

Likewise,

So,

Now differentiate with respect to

Plug in

Vasquez

Expert2022-01-09Added 669 answers

Using,

This is the derivative of

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