Page:Calculus Made Easy.pdf/45

Summary. Let us see how far we have got. We have arrived at the following rule: To differentiate ${\displaystyle x^{n}}$, multiply by the power and reduce the power by one, so giving us ${\displaystyle nx^{n-1}}$ as the result.

Exercises I. (See p. 254 for Answers.)

Differentiate the following:

(1) ${\displaystyle y=x^{13}}$	(2) ${\displaystyle y=x^{\tfrac {-3}{2}}}$
(3) ${\displaystyle y=x^{2a}}$	(4) ${\displaystyle u=t^{2\cdot 4}}$
(5) ${\displaystyle z={\sqrt[{3}]{u}}}$	(6) ${\displaystyle y={\sqrt[{3}]{x^{-5}}}}$
(7) ${\displaystyle u={\sqrt[{5}]{\tfrac {1}{x^{8}}}}}$	(8) ${\displaystyle y=2x^{a}}$
(9) ${\displaystyle y={\sqrt[{q}]{x^{3}}}}$	(10) ${\displaystyle y={\sqrt[{n}]{\tfrac {1}{x^{m}}}}}$

You have now learned how to differentiate powers of ${\displaystyle x}$. How easy it is!