Question

differentiate with respect to x
$3 {x}^{2} - \frac{4}{x}$
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Answer 1

Answer:

Given : y=(x−3)(x2+4)(◀+▶)−−−−−−−−−−−−−√.

Taking logarithm on both sides of (i), we get

logy=12{log(x−3)+log(x−3)+log(x2+4)−log(3x2+4x+5)}.

Differentiating both sides w.r.t. x, we get

1y.dydx=12.{1(x−3)+2x(x2+4)−(6x+4)(3x2+4x+5)}

⇒dydx=(12y).{1(x−3)+2x(x2+4)−(6x+4)(3x2+4x+5)}

=12.(x−3)(x2+4)(3x3+4x+4)−−−−−−−−−−−−−√.{1(x−3)+2x(x2+4)−(6x+4)(3x2+4x+5)}