# What is the derivative for y=tan(x)+x^(5/2)+2x?

May 2, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = {\sec}^{2} x + \frac{5}{2} {x}^{\frac{3}{2}} + 2$

#### Explanation:

$y = \tan x + {x}^{\frac{5}{2}} + 2 x$

color(green)(d/dxtanu=sec^2ucolor(blue)((du)/dxcolor(red)(rarr"Where u is a function of " x

color(green)(d/dxu^n=n*u^(n-1)color(blue)((du)/dxcolor(red)(rarr"Where u is a function of " x

dy/dx=color(green)(sec^2x)color(blue)(xx1)+color(green)(5/2x^(3/2))color(blue)(xx1)+color(green)(2color(blue)(xx1)

$= {\sec}^{2} x + \frac{5}{2} {x}^{\frac{3}{2}} + 2$