Find the derivative of f(x)= 2 sqrt x at x=4.
i thought that the derivative would be 2 x^1/2 but I guess this is wrong.
dy/dx 2x^(1/2)
2 * 1/2 x^(1/2 - 2/2)
2/2 x^(-1/2) = x^(-1/2) = 1/(sqrt(x))
You have two problems here.
1. need D:f(x) = 2sqrtx
2. subsitute x=4 into derivative
D: 2sqrtx :
a) multiply power times coefficient; 1/2 * 2 = 1
b)power - 1 = 1/2 -1 = -1/2
c. f'(x) = x^-1/2 or 1/sqrtx
substitute 4 for x and you should be there
To find the derivative of f(x) = 2√x, we can use the power rule for differentiation. The power rule states that if you have a function in the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).
In this case, we have f(x) = 2√x, which can also be written as f(x) = 2x^(1/2).
Applying the power rule, we differentiate each term separately:
f'(x) = 2 * (1/2) * x^((1/2) - 1)
Simplifying further:
f'(x) = x^(-1/2)
Now, to find the derivative at x = 4, we substitute the value of x into the derivative expression:
f'(4) = 4^(-1/2)
Simplifying this:
f'(4) = 1/√4
f'(4) = 1/2
Therefore, the derivative of f(x) = 2√x at x = 4 is 1/2.