Introduction to Derivative of Inverse Function Calculator

The derivative of an inverse function calculator is an online tool that you can use to calculate the rate of change of an inverse function. It provides you with an easy and fast way to calculate by doing simple clicks. It just needs an input function to perform the calculation.

The calculation of derivative of an inverse function is more complex than finding the derivative of a simple function. It is because the inverse function is expressed differently. Therefore, we introduce an online tool that can assist you in finding inverse function derivatives easily.

Formula used by inverse derivative calculator

An inverse function is any one-to-one function where it never takes the same value more than one time, i.e., there is only one y-value for every x-value. The derivative calculator uses this kind of function to calculate its derivative.

The derivative of an inverse function formula is expressed as;

$(f^{-1})'(x)=\frac {1}{f'f^{-1}(x)}$

This formula is derived by using the chain rule of differentiation as:

$f(f^{-1}(x))=x$

Applying derivative,

$\frac {d}{dx}f(f^{-1}(x))=\frac{d}{dx}(x)$

$f'(f^{-1}(x)).f^{-1}(x)=1$

Or,

$(f^{-1})'(x)=\frac{1}{f'f-1(x)}$

The derivative of the inverse function calculator uses the above formula to find the derivative of a function. It also helps you to determine the rate of change by providing you with the derivative graph of the function.

Inverse Function Derivative Example

Since the inverse function derivative formula is used to calculate derivatives of inverse function of any kind. Let's calculate the derivative of an inverse hyperbolic function cosh-1x. Suppose that,

$y=\DeclareMathOperator{\coth}{coth}\coth^{-1}x$

We can rearrange the above function as,

$\coth y=x$

Differentiating with respect to x

$\frac{d}{dx}(\coth y)=\frac{d}{dx}(x)$

Since the coth x derivative is -csch^2x.

$-\DeclareMathOperator{\csch}{csch}\csch^2 y\frac{dy}{dx}=1$

$\frac{dy}{dx}=-\frac{1}{\csch^2y}$

Since $y=\coth^{-1}x$

$\frac{dy}{dx}=-\frac{1}{\csch^2(\coth^{-1}x)}$

Now assume that $\theta =\coth^{-1}x$ and $\coth \theta =x$. Since

$\csch^y=1-\coth^2\theta=1-x^2$

Substituting in the derivative formula, we get

$\frac{dy}{dx}=\frac{-1}{1-x^2}$

Hence the derivative of coth inverse is $\frac{-1}{1-x^2}$

How to find Inverse Function Derivative Calculator online?

Finding a derivative calculator for an inverse function involves a few simple steps. The following steps will help you to search and use this online tool.

1. Open your preferred browser and navigate to the search engine google.
2. On the googel search bar, write the main keyword, inverse derivative calculator to search for this tool.
3. Google will provide you a list of different websites that offer derivative tools online.
4. Choose our derivatives of the inverse trig functions calculator from the list.

How does the Inverse Differentiation Calculator work?

The working of the inverse derivative calculator is based on the input function. It uses the implicit differentiation formula to calculate the derivative of an inverse function. It is because the inverse functions can also be treated as implicit functions.

When you provide an inverse function as input to this calculator, it analyzes the function and determines whether it is an inverse function. After analyzing the function, the inverse calculator provides you a step-by-step complete solution. If the function is not inverse, it computes the derivative using other derivative rules. 

Why use an inverse differentiation calculator?

Derivative calculator offers you this tool that has many applications for analytical and knowledge purposes. The main reason to use this calculator is that it provides a step-by-step solution for every input value, which makes it more reliable for you.

Since the inverse function is expressed in a complex form, i.e., in negative power, many students feel it difficult to calculate the derivative of such a function. So, it would be best for you to use our calculator, which allows you to calculate derivatives using the product rule calculator.

The results provided by this calculator are step-by-step and easy. It may help you to learn the derivative of the inverse function easily. Also, it provides all intermediate steps for you, along with the plots.

Benefits of using derivatives of inverse functions calculator

There are numerous benefits of using this tool. Some of these are listed below. It is easy to use because you just need to follow some simple steps to find the derivative of an inverse function.

• It is free to use so don’t pay for any premium tools.
• You can do practice with different examples to learn more about derivatives.
• It saves you from long-term calculations of derivatives, so you can learn more in less time.
• Inverse function derivative calculator provides you the calculations of inverse function’s derivative with 100% accurate solution.
• It is a reliable tool for inverse trigonometric differentiations.

How to use derivative of inverse trigonometric functions calculator

This only calculator requires only a good internal connection and some input values. You can easily perform differentiation by using this tool. We provide you with a step-by-step way to use this calculator. These steps are;

1. Enter the function in the relevant input box. In this step, you will need to write an inverse function that you want to differentiate.
2. Now select the variable of the derivative. Here you have to choose the variable by which the function is being differentiated.
3. Now review the function and click on the calculate button.

After clicking the calculate button, the derivative of the inverse trigonometric function calculator will provide you with the exact results within a few seconds. Also, it provides the derivative graph of the given function to visualize the rate of change.

Frequently asked questions

What is the derivative of inverse sine?

The derivative of the sine inverse function is written as (sin-1x)' = 1/√(1-x2), that is, the derivative of sin inverse x is 1/√(1-x2).

How do you find the derivative of an inverse function?

The derivative of an inverse function can be calculated by using chain rule of derivatives. For this, you can also write the function in reciprocal form. The inverse function derivative formula is,

$(f^{-1})'(x)=\frac{1}{f'f^{-1}(x)}$

What is an inverse function calculator?

The calculator for inverse functions determines the inverse of the given function. If a function f(x) is known, its inverse can be calculated by swapping the variables and writing x as a function of y, or x=f(y) x = f (y).