Derivative of ln{X^2 + 12}/7x ?

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Answer 1 · 2018-02-23T05:01:38

#(2x^2-ln(x^2+12)(x^2+12))/(7x^2(x^2+12))#

We are given: #d/dx((ln(x^2+12))/(7x))#

We can use the quotient rule here, which states that

#d/dx(x/y)=(x'y-xy')/y^2#

But, first we can take the constant out to get:

#1/7d/dx((ln(x^2+12))/(x))#

and so, here we go:

#=1/7[(x*(2x)/(x^2+12)-1*ln(x^2+12))/(x^2)]#

#=1/7[[(2x^2)/(x^2+12)-ln(x^2+12))/(x^2)]#

#=1/7[(2x^2-ln(x^2+12)(x^2+12))/(x^2(x^2+12))]#

#=(2x^2-ln(x^2+12)(x^2+12))/(7x^2(x^2+12))#