If `y=4x^4+2x^3+5/x+9`, then find `dy//dx`.

Explanation

`(dy)/(dx) = (d)/(dx)[4x^4+2x^3+5/x+9]`
(Differentiating both sides w.r.t. x)
`=(d)/(dx)[4x^4]+(d)/(dx)[2x^3]+(d)/(dx)[5/x]+(d(9))/(dx)`
(Using the property of linearity)
`=(d)/(dx)[4x^4]+(d)/(dx)[2x^3]+(d)/(dx)[5/x]`
(As differentiation of constant=0, `(d9)/(dx)=0`)
`=4(d)/(dx)[x^4]+2(d)/(dx)[x^3]+5(d)/(dx)[x^-1]`
(Separating constant coefficients)
`=4xx4x^3+2xx3x^2+5(-1)x^-2`
`=16x^3+6x^2-(5)/(x^2)`