Find the derivative of Y=1/√x?

Question

What is the thought process to get to the answer of -1/2x^3/2

Answer 1

This equation can be written as:

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.

Answer 2

If you rewrite 1/√x as x^(-1/2), it's easier to see how the derivative is found. (-1/2) x^(-1/2 - 1) or (-1/2)x^(-3/2). Hope this helps you. It's hard doing it on the computer without simply writing it.

Answer 3

think of it as y=x^(-1/2). Then you use the power rule where the new coefficient becomes 1*(-1/2) and the new exponent becomes -1/2 - 1, which is -3/2.

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))

Answer 4

The derivative is Y= -0.5(X^-1.5) using the formula below.
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)

Answer 5

Try multiplication.