Find the derivative of the function f by using the rules of differentiation.
f(u)=10/�ãu
f '(u) = ??
I will assume you meant to type
f(u) = 10/√u , but the font came out weird
f(u) = 10 u^(-1/2)
f'(u) = -5 u^(-3/2)
or -5/(√(u^3)
To find the derivative of the function f(u) = 10/√u using the rules of differentiation, we can follow these steps:
Step 1: Identify the function we want to differentiate. In this case, our function is f(u) = 10/√u.
Step 2: Apply the power rule for differentiation. The power rule states that if we have a function of the form f(u) = cu^n, where c is a constant and n is any real number, then the derivative is given by f'(u) = c * n * u^(n-1).
Step 3: Apply the power rule to our function. In our case, c = 10 and n = -1/2 (since √u is the same as u^(1/2)). Using the power rule, we have:
f'(u) = 10 * (-1/2) * u^(-1/2 - 1)
Simplifying this expression, we get:
f'(u) = -5u^(-3/2)
So, the derivative of the function f(u) = 10/√u is f'(u) = -5u^(-3/2).