Question:
Can anyone
take the first and second derivatives of y=3(x^2/3)-(x^2)?
Answer:
Given: Y = 3 ( X 2/3) – ( X2 )
1st and 2nd derivatives by
repeated application of the exponent rule
Y = X n
dY/dX = n * X n-1
1st derivative
dY/dX = 3 * 2/3 ( X 2/3 – 1) - ( 2 *
X 2 – 1) = 2 * X -1/ 3 2 * X
2nd derivative
d2Y / dX2 = 2 * (-1/3) * X
-1/3 – 1 – 2 *( 1 )* X 1-1 = -2/3 * X -4 / 3 2 (recall that X0
= 1)
More questions about
derivatives? Post them at THE MATH FORUM