How can I differentiate x with respect to x^2?

Answer 1

Let u = x^2. Then, x = +- SQRT(u)

dx/d(x^2) = +- d( SQRT(u) )/du = +- (1/2)u^(-1/2)

dx/d(x^2) = +- (1/2)/x = +- 1/2x

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Another method:

d(x^2)/dx = 2x. Then, dx/d(x^2) = 1/2x