`4xy + ln (x^2 y) = 7` Use implicit differentiation to find dy/dx

Friday, May 22, 2015

Find `(dy)/(dx) ` if ` 4xy+ln(x^2y)=7 `

Use properties of logarithms to rewrite the second term:

`4xy+2lnx+lny=7 `

Differentiate term by term with respect to x:

`4y+4x(dy)/(dx)+2/x+1/y(dy)/(dx)=0 `

`(dy)/(dx)(4x+1/y)=-(2/x+4y) `

`(dy)/(dx)=-(2/x+4y)/(4x+1/y) `

`(dy)/(dx)=-(2y+4xy^2)/(4x^2y+x) `

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