Q. 0 - Calculus

Question

Read the section and make your own summary of the material.

Step-by-Step Solution

Answer

The Chain Rule in Leibniz notation is written as follows.

$\frac{df}{dx}=\frac{df}{du}\frac{du}{dx}$

The Chain Rule in prime notation is written as follows.

$\left(f\circ u\right)\text{'}\left(x\right)=f\text{'}\left(u\left(x\right)\right)u\text{'}\left(x\right).$

Differentiating the implicit function with respect to any one variable is known as implicit differentiation.

Step 1. Given information.

The topic of the given section is The Chain Rule and Implicit Differentiation.

Step 2. Summary of section.

The Chain Rule in Leibniz notation is written as follows.

$\frac{df}{dx}=\frac{df}{du}\frac{du}{dx}$

The Chain Rule in prime notation is written as follows.

$\left(f\circ u\right)\text{'}\left(x\right)=f\text{'}\left(u\left(x\right)\right)u\text{'}\left(x\right).$

An implicit function is a function with more than one variable where one variable is a function of other variables and the expression of the function forms an equation by equating with zero or constant.

differentiating the implicit function with respect to any one variable is known as implicit differentiation.