(a) Explain what is meant by a composite function and illustrate your explanation…

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

(a) Explain what is meant by a composite function and illustrate your explanation with one example that is NOT the same as the one given in your textbook. (a) Explain what is meant by a composite function and illustrate your explanation with one example that is NOT the same as the one given in your textbook. (b) For the function

y = \sqrt{5x^{4}+2}

, (i) clearly identify an “inner” function

u(x)

and an “outer” function

f(u)

so that

y = f\bigl(u(x)\bigr)

, (ii) write

y

in the form

f(u)

using the functions you have chosen in part (i). (c) Using your identification from part (b), find

\displaystyle \frac{dy}{dx}

and simplify your final answer as far as possible.

Related theory

Composition of Functions
Functions
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability
Differentiation Rules

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