find the derivative of the function at the given number
F(x)= 1/ √x at 4
or
f(x) = x^(-1/2)
f ' (x) = (-1/2)x^(-3/2)
= (-1/2) /√(x^3)
sub in x = 4
thank you
To find the derivative of the function F(x) = 1/√x at the given number 4, we can use the rules of differentiation.
Step 1: Write the given function in a more simplified form.
F(x) = 1/√x = x^(-1/2)
Step 2: Use the power rule of differentiation, which states that if we have a function f(x) = x^n, then its derivative is f'(x) = n*x^(n-1).
Applying the power rule to our function F(x), we get:
F'(x) = (-1/2) * x^(-1/2 - 1)
= (-1/2) * x^(-3/2)
= -1 / (2 * √x^3 )
Step 3: Evaluate the derivative at the given number x = 4.
F'(4) = -1 / (2 * √4^3 )
= -1 / (2 * √64)
= -1 / (2 * 8)
= -1 / 16
So, the derivative of the function F(x) = 1/√x at x = 4 is -1/16.