The differentiation of e^tanx is equal to sec^{2}x e^{tanx}. In this post, we will learn how to differentiate e to the power tanx with respect to x.

The following two formulas will be used to find the derivative of e^{tanx}.

- d/dx(tanx) = sec
^{2}x. - log
_{a}a^{k }=k.

Now, we will learn to find the derivative of e to the power tanx with respect to x.

**How to Find the derivative of e**^{tanx}

^{tanx}

**Question**: How to differentiate e^{tanx}?

**Solution:**

Let y= e^{tanx}

Taking natural logarithms on both sides, we get that (natural logarithm means the logarithm with base e, i.e. log_{e})

log y = tanx (here we used the logarithm rule log_{e}e^{k} =k.)

Now, differentiate both sides with respect to x. This will give us

$\dfrac{1}{y} \dfrac{dy}{dx}$ = sec^{2}x as we know that the derivative of tanx is sec^{2}x.

⇒ $\dfrac{dy}{dx}$ = y sec^{2}x

Putting the value of y, that is, y=e^{tanx}, we get from above that

$\dfrac{d}{dx}$(e^{tanx}) = sec^{2}x e^{tanx}.

**Thus, the differentiation of e ^{tanx} with respect to x is equal to e^{tanx} sec^{2}x.**

**Video solution on derivative of e ^{tanx}:**

**ALSO READ:**

Derivative of arc(cotx): The derivative of arc(cotx) is -1/(1+x^{2}).

Differentiate e^{sinx}: The derivative of e^{sinx} is e^{sinx} cosx.

Differentiate e^{cosx}: The derivative of e^{cosx} is -e^{cosx} sinx.

## FAQs

### Q1: What is the derivative of e^{tanx}?

Answer: The derivative of e^tanx is equal to sec^{2}x e^{tanx}.

### Q2: If y=e^{tanx}, then find dy/dx?

Answer: If y=e^{tanx}, then dy/dx = sec^{2}x e^{tanx}.