Question

Differentiate the following w.r.t.x. :

y = `x^2sqrt(x) + x^4logx`

Answer 1

y = `x^2sqrt(x) + x^4logx`

Differentiating w.r.t. x, we get

`("d"y)/("d"x) = "d"/("d"x) (x^2 sqrt(x) + x^4 log x)`

`("d"y)/("d"x) = "d"/("d"x) (x^(5/2)) + "d"/("d"x) (x^4 log * x)`

= `5/2x^(5/2 - 1) + [x^4 "d"/("d"x) log x + log x("d"/("d"x) x^4)]`

= `5/2x^(3/2) + [x^4 (1/x) + log x(4x^3)]`

= `5/2x^(3/2) + x^3 (1 + 4logx)`