# How do you find the derivative of r(x)= (0.3x^2-4.2x+9.2)^1.5?

Mar 15, 2016

$r ' \left(x\right) = \left(0.9 x - 6.3\right) \sqrt{0.3 {x}^{2} - 4.2 x + 9.2}$

#### Explanation:

$r \left(x\right) = {\left(0.3 {x}^{2} - 4.2 x + 9.2\right)}^{1.5}$

$r \left(x\right) = {\left(0.3 {x}^{2} - 4.2 x + 9.2\right)}^{\frac{3}{2}}$

$r ' \left(x\right) = \frac{3}{2} {\left(0.3 {x}^{2} - 4.2 x + 9.2\right)}^{\frac{1}{2}} \cdot \left(0.3 {x}^{2} - 4.2 x + 9.2\right) '$

$r ' \left(x\right) = \frac{3}{2} {\left(0.3 {x}^{2} - 4.2 x + 9.2\right)}^{\frac{1}{2}} \cdot \left(0.6 x - 4.2\right)$

$r ' \left(x\right) = \left(0.9 x - 6.3\right) \sqrt{0.3 {x}^{2} - 4.2 x + 9.2}$