Enter your function and the variable for which you want to calculate the second derivative using implicit differentiation into the calculator.
Implicit Differentiation Formula
The following formula is used to calculate the second derivative using implicit differentiation.
\(\frac{d^2 y}{dx^2} = \frac{d}{dx}\left(\frac{dy}{dx}\right)\)
Variables:
- \(\frac{d^2 y}{dx^2}\) is the second derivative of \(y\) with respect to \(x\)
- \(\frac{dy}{dx}\) is the first derivative of \(y\) with respect to \(x\)
To calculate the second derivative, first find the first derivative using implicit differentiation, then differentiate again with respect to \(x\).
What is Implicit Differentiation?
Implicit differentiation is a technique used to differentiate equations that are not explicitly solved for one variable in terms of another. It is particularly useful for finding the derivatives of functions that are defined implicitly, rather than explicitly. In cases where the relationship between variables is given by an equation, implicit differentiation allows us to find derivatives without needing to solve for one variable explicitly.
How to Calculate the Second Derivative?
The following steps outline how to calculate the second derivative using implicit differentiation.