How do you find the derivative of $y = x^{4} {(2 x - 5)}^{6}$ $y = x^4(2x - 5)^6$ ?

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Answer 1 · 2016-10-08T04:35:16

$y'=u'v+v'u$ - product rule

Let $u=x^4$ and $v=(2x-5)^6$
$u'=4x^3$
$v'=2*6(2x-5)^5=12(2x-5)^5->$ by chain rule

Subbing into $y'=u'v+v'u$ ,

$y'=4x^3(2x-5)^6+12(2x-5)^5x^4$

Simplifying,

$y'=x^3(2x-5)^5(4(2x-5)+12x)=x^3(2x-5)^5(20x-20)$

How do you find the derivative of y = x^4(2x - 5)^6y=x4(2x−5)6y = x^4(2x - 5)^6?