# [Solved] What is the Derivative of 10^x [10 to the x]?

The derivative of 10x is equal to 10x ln 10. Here ln denotes the logarithm with base e, called the natural logarithm. In this post, we will learn to compute the derivative of 10 raised to x.

## Derivative of 10x

Question: What is the derivative of 10x?

Answer: The derivative of 10x is 10x ln 10.

Explanation:

To find the derivative of 10 to the x, we will use the logarithmic differentiation. Let us put

y=10x

We need to find $\dfrac{dy}{dx}$. Taking logarithm on both sides with base 10, we get that

$\log_{10} y =\log_{10} 10^x$

⇒ $\log_{10} y =x$ as we know that loga ak=k.

Differentiating both sides with respect to x, we obtain that

$\dfrac{d}{dx}(\log_{10} y)=\dfrac{dx}{dx}$

⇒ $\dfrac{1}{\log_e 10} \dfrac{1}{y} \dfrac{dy}{dx}=1$

⇒ $\dfrac{dy}{dx}=y \cdot \log_e 10$

⇒ $\dfrac{dy}{dx}=10^x \cdot \ln 10$ as y=10x and loge=ln

Thus, the derivative of 10x is 10x ln 10.

## Question-Answer on Derivative of 10x

Question: What is the derivative of 10x at x=0?

From the above, we have that the derivative of 10x is 10x ln 10. That is,

$\dfrac{d}{dx}(10^x)=[10^x \ln 10]_{x=0}$

= 100 ln 10

= 1 × ln 10 as we know that a0=1 for any non-zero number a.

= ln 10

So the derivative of 10 raised to x at x=0 is equal to ln10.

Derivative of 2x

Derivative of 1/logx

Derivative of mod x

## FAQs

Q1: If y=10x, then find dy/dx?

Answer: As the derivative of 10x is 10x ln 10, we have that dy/dx=10x ln 10.