Y = x^(-1/2)

The derivative of anything that looks like X^K is K*X^(K-1)

Substitute K = -1/2 and you get your result.

This should have been the first thing you learned about derivatives.

Now youve got -1/2 x ^ (-3/2), but you can rewrite the negative exponent as a fraction with a numerator of 1, so you’ve got

-1/2 * 1/x^(3/2) = -1/(2*x^(3/2))

The formula is Y=X^j

j= -0.5

The answer is dY/dX=j*X^(j-1)

Y=X^j

Y+delta Y = (X+ delta X)^j

delta Y = [(X+ delta X)^j]-X^j

(delta Y)/delta X = {[(X+ delta X)^j]-X^j}/delta X

(delta Y)/delta X = {[X^j+j*delta X*X^(j-1)+…]-X^j}/ delta X

lim (delta Y)/delta X = j*X^(j-1)

dY/dX= j*X^(j-1)