Q. 5 Write down a rule for differenti... [FREE SOLUTION]

Chapter 2: Q. 5 (page 209)

Write down a rule for differentiating a composition $f (u (v (w (x))))$ of four functions
(a) in 鈥減rime鈥� notation and
(b) in Leibniz notation.

Short Answer

Expert verified

(a) in 鈥減rime鈥� notation the derivative is: $(f 鈭� u 鈭� v 鈭� w)' (x) = f' (u 鈭� v 鈭� w) (x) 脳 u' (v 鈭� w) (x) 脳 v' (w (x)) 脳 w' (x)$

(b) in Leibniz notation the derivative is: $\frac{d f}{d x} = \frac{d f}{d u} 脳 \frac{d u}{d v} 脳 \frac{d v}{d w} 脳 \frac{d w}{d x}$

Step by step solution

Step 1. Given information:

The composite function is;

$f (u (v (w (x))))$

Part (a). Step 1. Derivative in prime notation:

The derivative of the given function in prime notation is; $(f 鈭� u 鈭� v 鈭� w)' (x) = f' (u 鈭� v 鈭� w) (x) 脳 u' (v 鈭� w) (x) 脳 v' (w (x)) 脳 w' (x)$

Part (b). Step 1. Derivative in Leibniz notation:

In Leibniz notation the derivative of the function is:

$\frac{d f}{d x} = \frac{d f}{d u} 脳 \frac{d u}{d v} 脳 \frac{d v}{d w} 脳 \frac{d w}{d x}$

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91影视

Write down a rule for differentiating a composition $f (u (v (w (x))))$ of four functions
(a) in 鈥減rime鈥� notation and
(b) in Leibniz notation.

Short Answer

Step by step solution

Step 1. Given information:

Part (a). Step 1. Derivative in prime notation:

Part (b). Step 1. Derivative in Leibniz notation:

One App. One Place for Learning.

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Recommended explanations on Math Textbooks

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91影视

Write down a rule for differentiating a composition f(u(v(w(x))))of four functions(a) in 鈥減rime鈥� notation and(b) in Leibniz notation.

Short Answer

Step by step solution

Step 1. Given information:

Part (a). Step 1. Derivative in prime notation:

Part (b). Step 1. Derivative in Leibniz notation:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Discrete Mathematics

Geometry

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Write down a rule for differentiating a composition $f (u (v (w (x))))$ of four functions
(a) in 鈥減rime鈥� notation and
(b) in Leibniz notation.