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Q. 3

Expert-verified

Calculus

Found in: Page 209

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

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

a) In prime notation the derivative is $(g \circ h)' (x) = g' (h (x)) \times h' (x)$

b) In Leibniz notation the derivative is: $\frac{d g}{d x} = \frac{d g}{d h} \times \frac{d h}{d x}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information:

The composite function is:

$g (h (x))$

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

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

$(g \circ h)' (x) = g' (h (x)) \times h' (x)$

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

In Leibniz notation, the derivative is:

$\frac{d g}{d x} = \frac{d g}{d h} \times \frac{d h}{d x}$

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