How do I find the derivative of $y= ln(4 x)/x^7$ ?

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Answer 1 · 2016-01-10T19:04:44

$dy/dx=(1-7ln(4x))/x^8$

The quotient rule states that

$d/dx [(f(x))/(g(x))]=(g(x)*f'(x)-f(x)*g'(x))/([g(x)]^2)$ .

Application of this rule to the given function yields :

$dy/dx=(x^7(4/(4x))-7x^6*ln(4x))/(x^7)^2$

$=(x^6(1-7ln(4x)))/x^14$

$=(1-7ln(4x))/x^8$ .

How do I find the derivative of y= ln(4 x)/x^7y= ln(4 x)/x^7?