Solved: "What is the derivative of 10x?"

Pam Stokes

Answered question

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}{d x} [a^{u}] = (\ln a) \cdot (a^{u}) \cdot \frac{d u}{d x}

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,

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

We have,

\ln (a^{b}) = b \ln a

Likewise,

\ln (10^{x}) = x \ln 10

So,

\ln y = x \ln 10

Now differentiate with respect to

x

\frac{1}{y} \cdot \frac{d y}{d x} = \ln 10

\frac{d y}{d x} = y \ln 10

Plug in

y = 10^{x}

\frac{d y}{d x} = 10^{x} \ln 10

Vasquez

Expert2022-01-09Added 669 answers

Using, $\frac{d}{d x} (a^{x}) = a^{x} \log a$
$\frac{d}{d x} (10^{x}) = 10^{x} \log 10$
This is the derivative of $y = 10^{x}$

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