What is the derivative of #(2ln(x+3))/x^2#?

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What is the derivative of #(2ln(x+3))/x^2#?

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Answer 1 · 2018-04-01T16:29:40

answer = #"-2(x+6)"/x^3#

Explanation:

#d/dx(u/v)="u'v-v'u"/v^2#
similarly, #d/dx((2(x+3))/x^2)=d/dx((2x+6)/x^2)#
=#((x^2)d/dx(2x+6)-(2x+6)d/dx(x^2))/(x^2)^2#
=#((x^2)(2)-(2x+6)(2x))/x^4#
=#(2x^2-4x^2-12x)/x^4#
#(-2x^2-12x)/x^4#
#(-2x(x+6))/x^4=(-2(x+6))/x^3#

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What is the derivative of #(2ln(x+3))/x^2#?

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