Mixed elementary and composite derivatives

Text

Compute the derivative of each function:

• (a) $y=x^{4}-3x^{2}+7$
• (b) $y=(2x-1)^{5}$
• (c) $y=\dfrac{1}{x^{2}+1}$
• (d) $y=x\sqrt{x+1}$

Solution

• (a) $y'=4x^{3}-6x$.
• (b) $y'=10(2x-1)^{4}$.
• (c) $y'=-\dfrac{2x}{(x^{2}+1)^{2}}$.
• (d) $y'=\sqrt{x+1}+\dfrac{x}{2\sqrt{x+1}}=\dfrac{3x+2}{2\sqrt{x+1}}$.