Question

Differentiate the function w.r.t.x:
(4x² - 7x + 5). sec x

Answer 1

HOPE IT HELPS U ✌️✌️

Answer 2

We know that

$\frac{d {x}^{n} }{dx} = n {x}^{n - 1} \\ \\ \frac{d \: sec\: x}{dx} = sec\: x\:tan\:x$
So, to differentiate given function with respect to x, we have to apply UV formula of differentiation.

$\frac{d(UV)}{dx} = U \frac{dV}{dx} + V\frac{dU}{dx} \\ \\ here \: U = (4{x}^{2}-7x+5) \\ \\ V = sec \: x \\ \\ \frac{d[(4{x}^{2}-7x+5) \: sec\: x]}{dx} =\\\\ (4{x}^{2}-7x+5) \bigg(\frac{d \: sec \: x}{dx}\bigg) + sec \: x\bigg(\frac{d (4{x}^{2}-7x+5) }{dx}\bigg) \\ \\\frac{d[ (4{x}^{2}-7x+5) \: sec\: x]}{dx}\\\\ = (4{x}^{2}-7x+5) sec\: x\:tan\:x + sec\: x(8x-7)$
Hope it helps you