The differentiation of e to the sin^{-1}x is equal to 1/√(1-x^{2}) e^{sin^{-1}x}. In this post, we will learn how to differentiate e to power sin inverse x with respect to x.

Let us find the derivative of e^{sin^{-1}x} with respect to x.

**Find the derivative of e^{sin**^{-1}x}

^{-1}x}

**Question**: How to differentiate e^{sin^{-1}x}?

**Solution:**

Let y= $e^{\sin^{-1}x}$

Taking natural logarithms [ln=log_{e}] on both sides, we get that

ln y = sin^{-1}x as we know that ln e^{k} =k.

Differentiate both sides with respect to x. This will give us

$\dfrac{1}{y} \dfrac{dy}{dx}$ = $\dfrac{1}{\sqrt{1-x^2}}$, because the derivative of sin^{-1}x is 1/√(1-x^{2}).

⇒ $\dfrac{dy}{dx}$ = $\dfrac{y}{\sqrt{1-x^2}}$

Putting the value of y, that is, y=e^{sin^{-1}x}, we get that

$\dfrac{d}{dx} \Big(e^{\sin^{-1}x} \Big)$ = $e^{\sin^{-1}x} \dfrac{1}{\sqrt{1-x^2}}$.

**Thus, the differentiation of e to the power sin inverse x with respect to x is equal to e ^{sin-1x} 1/√(1-x^{2}).**

**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.

Differentiate e^{tanx}: The derivative of e^{tanx} is e^{tanx} sec^{2}x.

## FAQs

### Q1: What is the derivative of e to the power sin inverse x?

Answer: The derivative of e to the power sin^{-1}x is equal to e^{sin-1x} 1/√(1-x^{2}).

### Q2: If y=e^{sin-1x}, then find dy/dx?

Answer: If y=e^{sin-1x}, then dy/dx = e^{sin-1x} 1/√(1-x^{2}).