let's skip some of those brackets for easier reading,
((x^2)-((3x^2)(ln(4x))))/(x^6)
= [ x^2 - 3x^2 ln(4x) ]/ x^6
= [ 1 - 3 ln(4x) ] / x^4
= x^-4 - (3x^-4)(ln (4x))
dy/dx = -4x^-5 - ( (3x^-4)(1/x) - (12x^-5)ln(4x) )
= -4x^-5 - 3x^-5 + 12x^-5(ln(4x))
= x^-5( -4 -3 + 12ln(4x))
= -(7 - 12ln(4x))/x^5
or
= (12ln(4x) - 7)/x^5
confirmation:
http://www.wolframalpha.com/input/?i=dy%2Fdx+for++y%3D+((x%5E2)-((3x%5E2)(ln(4x))))%2F(x%5E6)
Differentiate the function.((x^2)-((3x^2)(ln(4x))))/(x^6)
2 answers
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