Chapter 2: Q. 4 (page 209)

In the text we noted that if $f (u (v (x)))$ was a composition of three functions, then its derivative is $\frac{d f}{d x} = \frac{d f}{d u} \times \frac{d u}{d v} \times \frac{d v}{d x}$ . Write this rule in “prime” notation.

Short Answer

Expert verified

In prime notation the derivative is:

$(f \circ u \circ v)' (x) = f' (u \circ v) (x) \times (u \circ v)' (x) \times v' (x)$

Step by step solution

Step 1. Given information:

The composite function and its derivative are:

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

$\frac{d f}{d x} = \frac{d f}{d u} \times \frac{d u}{d v} \times \frac{d v}{d x}$

Step 2. Derivative in the prime notation:

The derivative of the given composite function is written as:

(f \circ u \circ v)' (x) = f' (u \circ v) (x) \times (u \circ v)' (x) \times v' (x)

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In the text we noted that if $f (u (v (x)))$ was a composition of three functions, then its derivative is $\frac{d f}{d x} = \frac{d f}{d u} \times \frac{d u}{d v} \times \frac{d v}{d x}$ . Write this rule in “prime” notation.

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Derivative in the prime notation:

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In the text we noted that if f(u(v(x))) was a composition of three functions, then its derivative is dfdx=dfdu×dudv×dvdx. Write this rule in “prime” notation.

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Derivative in the prime notation:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

In the text we noted that if $f (u (v (x)))$ was a composition of three functions, then its derivative is $\frac{d f}{d x} = \frac{d f}{d u} \times \frac{d u}{d v} \times \frac{d v}{d x}$ . Write this rule in “prime” notation.