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Question
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Solution
Let y =`logx/(x^3-5)`
Differentiating w.r.t. x, we get
`dy/dx= d/dx(logx/(x^3 - 5))`
= `((x^3 - 5)d/dx(logx) - (logx)d/dx(x^3 - 5))/((x^3 - 5)^2)`
=`((x^3 - 5)(1/x) - logx(d/dx(x^3) - d/dx(5)))/((x^3 - 5)^2)`
= `((x^3 - 5)1/x - logx(3x^2 - 0))/((x^3 - 5)^2)`
= `((x^3 - 5)1/x - log x * 3x^2)/(x^3 - 5)^2`
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