Question

Differentiate 4x2 -1 / (5-2x)3
x= 2

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Answer 1

$\sf { \frac{dy}{dx} = \frac{4x^{2} -1}{(5-2x)3 } }$

Using quotient rule:

$\sf { \frac{dv}{du} = \frac{ \frac{dv}{du} . u - \frac{du}{dv} . v}{u^{2} } }$

Final steps:

$\sf { \frac{ 8x. (15-6x) - (- 6).(4x^{2} -1) }{(15-6x)^{2} } }$

$\sf { \frac{120x - 24x^{2} -6}{(15-6x)^{2} } }$

For x = 2:

Put 2 in place of x, in the final equation.

» $\boxed {\sf {Differentiation = \frac{46}{27} }}$