Question

Differentiate the following w. r. t. x. : `x^(5/2) e^x`

Answer 1

Let y = `x^(5/2) "e"^x`

Differentiating w.r.t. x, we get

`dy/dx = d/dx(x^(5/2)"e"^x)`

= `x^(5/2)d/dx("e"^x)+ "e"^x d/dx(x^(5/2))`

= `x^(5/2) ("e"^x) + "e"^x(5/2x^(3/2))`

= `"e"^x(x^(5/2)+ 5/2 x^(3/2))`