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