# How do you find the derivative of -7x^5(sqrt(x)) + (4/(x^2(sqrt(x))))?

Jul 2, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{77}{2} \sqrt{{x}^{9}} - \frac{10}{\sqrt{{x}^{7}}}$

#### Explanation:

Write as: $y = \left(- 7 {x}^{5} \times {x}^{\frac{1}{2}}\right) + \left(4 \times {x}^{- 2} \times {x}^{- \frac{1}{2}}\right)$

$y = - 7 {x}^{\frac{11}{2}} + 4 {x}^{- \frac{5}{2}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(- 7 \times \frac{11}{2} \times {x}^{\frac{11}{2} - 1}\right) + \left(4 \times \left(- \frac{5}{2}\right) \times {x}^{- \frac{5}{2} - 1}\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{77}{2} {x}^{\frac{9}{2}} - 10 {x}^{- \frac{7}{2}}$

Writing this in the same form as the question:

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{77}{2} \sqrt{{x}^{9}} - \frac{10}{\sqrt{{x}^{7}}}$