# How do you find the derivative of f(x)=(x^2+5x-3)(x^5-6x^3+3x^2-7x+1)?

Jan 27, 2017

See below

#### Explanation:

You would have to use the product rule to differentiate this function, or you could open up the brackets, but this would take much longer.

Product rule:

$\frac{d}{\mathrm{dx}} u v = u \frac{\mathrm{dv}}{\mathrm{dx}} + v \frac{\mathrm{du}}{\mathrm{dx}}$

$\frac{d}{\mathrm{dx}} f \left(x\right) = \left(2 x + 5\right) \left({x}^{5} - 6 {x}^{3} + 3 {x}^{2} - 7 x + 1\right) + \left(5 x - 18 {x}^{2} + 6 x - 7\right) \left({x}^{2} + 5 x - 3\right)$