Question

Найдите f ` (1), если f(x)=4√x-5

Answer 1

Если 5 под корнем, то решений нет.
f'(x)=2\(√x)
f'(1)=2

Answer 2

To find the derivative of the given function f(x) = 4√x - 5 and evaluate it at x = 1, we can use the power rule for differentiation.

The power rule states that if we have a function of the form f(x) = x^n, where n is a constant, then the derivative is given by f'(x) = n*x^(n-1).

Let's apply the power rule to find the derivative of f(x) = 4√x - 5:

f'(x) = d/dx (4√x - 5) = d/dx (4x^(1/2) - 5) = 4 * (1/2) * x^(-1/2) = 2x^(-1/2)

Now, let's evaluate f'(x) at x = 1:

f'(1) = 2(1)^(-1/2) = 2/√1 = 2/1 = 2

Therefore, f'(1) = 2.