A student concludes that the derivative of is

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

Problem

A student concludes that the derivative of

h(x)=x^{3/4}

(3/4)x^{1/4}

. Which of the following best evaluates the student’s conclusion? (a) The student is incorrect; the correct derivative is

\dfrac{4}{3}x^{-1/4}

because you divide by the exponent rather than multiply. (b) The student is incorrect; the correct derivative is

\dfrac{3}{4}x^{-1/4}

because the exponent should decrease by

1

, not increase. (c) The student is correct; after applying the power rule one obtains

\dfrac{3}{4}x^{1/4}

since

3/4-1=1/4

.},{ (d) The student is incorrect because differentiating fractional powers always requires the chain rule instead of the simple power rule.