William Burnett

2021-12-30

What is the derivative of $5}^{x$ ?

Laura Worden

Beginner2021-12-31Added 45 answers

Explanation:

Given:$\frac{d}{dx}\left({5}^{x}\right)$

Apply the general formula that$\frac{d}{dx}\left({a}^{x}\right)={a}^{x}\mathrm{ln}a\text{}\text{for}\text{}\in \mathbb{R}$

$\therefore \frac{d}{dx}\left({5}^{x}\right)={5}^{x}\mathrm{ln}5$

Given:

Apply the general formula that

Maria Lopez

Beginner2022-01-01Added 32 answers

Explanation:

Let$y={5}^{x}$

differentiate implicity with respect to x

take$\mathrm{ln}$ (natural log) of both sides

$\mathrm{ln}y={\mathrm{ln}5}^{x}=x\mathrm{ln}5$

$\Rightarrow \frac{1}{y}\frac{dy}{dx}=\mathrm{ln}5$

$\Rightarrow \frac{dy}{dx}=y\mathrm{ln}5={5}^{x}\mathrm{ln}5$

Let

differentiate implicity with respect to x

take

nick1337

Expert2022-01-08Added 573 answers

For a generalized answer to this question, you can use the following which works in cases of

So

And, likewise:

Note