Inverse trigonometric functions differentiation Calculator

Get detailed solutions to your math problems with our Inverse trigonometric functions differentiation step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

ddx (arcsin(4x²))

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 Example

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Here, we show you a step-by-step solved example of inverse trigonometric functions differentiation. This solution was automatically generated by our smart calculator:

\frac{d}{dx}\left(\arcsin\left(4x^2\right)\right)

Taking the derivative of arcsine

\frac{1}{\sqrt{1-\left(4x^2\right)^2}}\frac{d}{dx}\left(4x^2\right)

The power of a product is equal to the product of it's factors raised to the same power

\frac{1}{\sqrt{1-4^2\left(x^2\right)^2}}\frac{d}{dx}\left(4x^2\right)

Calculate the power $4^2$

\frac{1}{\sqrt{1-16\left(x^2\right)^2}}\frac{d}{dx}\left(4x^2\right)

Simplify $\left(x^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$ . In the expression, $m$ equals $2$ and $n$ equals $2$

16x^{2\cdot 2}

Multiply $2$ times $2$

16x^{4}

Multiply $2$ times $2$

\frac{1}{\sqrt{1-16x^{4}}}\frac{d}{dx}\left(4x^2\right)

The power of a product is equal to the product of it's factors raised to the same power

\frac{1}{\sqrt{1- 16x^{4}}}\frac{d}{dx}\left(4x^2\right)

Multiply $-1$ times $16$

\frac{1}{\sqrt{1-16x^{4}}}\frac{d}{dx}\left(4x^2\right)

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

4\left(\frac{1}{\sqrt{1-16x^{4}}}\right)\frac{d}{dx}\left(x^2\right)

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$ , then $f'(x) = nx^{n-1}$

8\left(\frac{1}{\sqrt{1-16x^{4}}}\right)x^{\left(2-1\right)}

Subtract the values $2$ and $-1$

8\left(\frac{1}{\sqrt{1-16x^{4}}}\right)x

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$ , then $f'(x) = nx^{n-1}$

4\cdot 2\left(\frac{1}{\sqrt{1-16x^{4}}}\right)x

Multiply $4$ times $2$

8\left(\frac{1}{\sqrt{1-16x^{4}}}\right)x

Multiply the fraction by the term

\frac{8\cdot 1x}{\sqrt{1-16x^{4}}}

Any expression multiplied by $1$ is equal to itself

\frac{8x}{\sqrt{1-16x^{4}}}

Multiply the fraction by the term

\frac{8x}{\sqrt{1-16x^{4}}}

 Final answer to the exercise

\frac{8x}{\sqrt{1-16x^{4}}}

Inverse trigonometric functions differentiation Calculator

Get detailed solutions to your math problems with our Inverse trigonometric functions differentiation step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

 Example

 Solved Problems

 Difficult Problems

 Final answer to the exercise

Are you struggling with math?

 Popular problems

Inverse trigonometric functions differentiation Calculator

Get detailed solutions to your math problems with our Inverse trigonometric functions differentiation step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

 Example

 Solved Problems

 Difficult Problems

 Final answer to the exercise

Are you struggling with math?

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 Popular problems