Question

(√x)(X-3)³ using product rule find dy/dx

Answer 1

~ DiferentiaL

Hi There , hope this can help you :

Let :

$u = \sqrt{x} = > \frac{du}{dx} = \frac{1}{2 \sqrt{x} } \\ v = {(x - 3)}^{3} = > \frac{dv}{dx} = 3(x - 3)$

Use the multiplication formula of Diferentiation

$\frac{dy}{dx} = \frac{du}{dx} .v + \frac{dv}{dx} .u \\ \frac{dy}{dx} = \frac{1}{ 2\sqrt{x} } {(x - 3)}^{3} + \sqrt{x} (3(x - 3)^{2} ) \\ \frac{dy}{dx} = \frac{ {(x - 3)}^{3} }{ 2\sqrt{x} } + 3 \sqrt{x} {(x - 3)}^{2} \\ \frac{dy}{dx} = {(x - 3)}^{2} ( \frac{x - 3}{2 \sqrt{x} } + 3 \sqrt{x} )$