Solveeit Logo

Question

Question: If y = x – x<sup>2</sup>, then the derivative of y<sup>2</sup> w.r.t. x<sup>2</sup> is-...

If y = x – x2, then the derivative of y2 w.r.t. x2 is-

A

2x2 + 3x – 1

B

2x2 – 3x + 1

C

2x2 + 3x + 1

D

None of these

Answer

2x2 – 3x + 1

Explanation

Solution

d(y2)d(x2)\frac{d(y^{2})}{d(x^{2})} = 2y.dydx2x\frac{2y.\frac{dy}{dx}}{2x} = (xx2)×(12x)x\frac{(x - x^{2}) \times (1 - 2x)}{x}

= (1 – x) (1 – 2x)

= 2x2 – 3x + 1