Which of the following best explains why differentiating requires more than one…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Which of the following best explains why differentiating

y = x^{2}\cos(x^{3})

requires more than one differentiation rule? (a) Because

y

is simply the product of

x^{2}

and

\cos(x^{3})

, so only the product rule is necessary. (b) Because

y

is the product of

x^{2}

and

\cos(x^{3})

, and the cosine term contains the inner function

x^{3}

. (c) Because

y

is a quotient of two functions, so the quotient rule must be applied. (d) Because

y

can be viewed as the composition

[\cos(x)]^{3}

, requiring only the chain rule.