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Q. 3

Expert-verified
Found in: Page 209

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# State the chain rule for differentiating a composition $g\left(h\left(x\right)\right)$ of two functions expressed (a) in “prime” notation and (b) in Leibniz notation.

a) In prime notation the derivative is $\left(g\circ h\right)\text{'}\left(x\right)=g\text{'}\left(h\left(x\right)\right)×h\text{'}\left(x\right)$

b) In Leibniz notation the derivative is:$\frac{dg}{dx}=\frac{dg}{dh}×\frac{dh}{dx}$

See the step by step solution

## Step 1. Given information:

The composite function is:

$g\left(h\left(x\right)\right)$

## Part (a). Step 1. The derivative in prime notation:

In prime notation the derivative of the function is written as:

$\left(g\circ h\right)\text{'}\left(x\right)=g\text{'}\left(h\left(x\right)\right)×h\text{'}\left(x\right)$

## Part (b). Step 1. The derivative in Leibniz notation:

In Leibniz notation, the derivative is:

$\frac{dg}{dx}=\frac{dg}{dh}×\frac{dh}{dx}$