Question

Differentiate the following w. r. t. x. : `sqrtx (x^2 + 1)^2`

Answer 1

Let y = `sqrtx (x^2 + 1)^2`

∴ `y = x^(1/2) (x^4 + 2x^2 + 1)`

y = `x^(9/2) + 2x^(5/2) + x^(1/2)`

Differentiating w.r.t. x, we get

`dy/dx = d/dx (x^(9/2) + 2x^(5/2) + x^(1/2))`

= `d/dx x^(9/2) + 2d/dxx^(5/2) + d/dxsqrtx`

= `9/2 x^(9/2-1) + 2xx 5/2 x^(5/2-1)+1/(2sqrtx)`

= `9/2 x^(7/2) + 5x^(3/2) + 1/(2sqrtx)`