To find the derivative of y = x^3/3 - 2sqrtx at x =
3.
To find dy/dx at x= 3 , we first find the derivative
.Then find its value at x=3.
Let f(x) = y = x^3/3 -
2sqrtx.
f'(x) = dy/dx = {x^3/3 -
2x^(1/2)}'
dy/dx = (x^3/3)' -
2(x^1/2)'.
We use (cx^n)' =cn*x^(n-1) , where c is any
constant but not zero.
dy/dx = 3*x^2/3 -
2(1/2)x^(1/2-1)
dy/dx = f'(x) =
x^2-1/x^(1/2)
f'(3) =
3^2-1/3^(1/2)
f'(3) = 9 -(sqrt3)/3.
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