Derivative Rules

10 practice questionsCalculus IStep-by-step solutions

Try a few

The revenue from selling $x$ units of a product is given by $R(x) = (5x + 2)(\sqrt{x} - 1)$ . Find the marginal revenue $R'(4)$ .

5

16

\frac{21}{2}

10.5

dollars per unit

22

The position of a moving object is given by $s(t) = \frac{(t^2 + 1) \sqrt{t}}{t^3 + 2}$ . Find the velocity $v(1) = s'(1)$ .

A.-

\frac{1}{3}

\frac{2}{3}

\frac{1}{3}

units/s

1

Differentiate the function $f(x) = \frac{(x^2+1)(2x-3)}{\sqrt{x}}$ with respect to $x$ .

\frac{10x^3 - 9x^2 + 2x + 3}{x^{3/2}}

\frac{10x^3 - 9x^2 + 2x + 3}{2x^{3/2}}

\frac{10x^3 - 9x^2 + 2x + 3}{2x}

\frac{10x^3 - 9x^2 + 2x}{2x^{3/2}}

All 10 questions with worked solutions, an AI tutor that explains every step, and games that make the drilling stick. Free to start.

No card needed · 10 free AI questions daily