Question

Найдите производную функции y=1/корень из x

Answer 1

-1/x^2*1/2*корень из x =-1/2x^2*корень из x

Answer 2

Calculating the Derivative of y = 1/√x

To find the derivative of the function y = 1/√x, we can use the power rule and the chain rule. Let's break it down step by step:

1. Rewrite the function using exponent notation: y = x^(-1/2)

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

Applying the power rule to our function, we get: y' = (-1/2) * x^(-1/2 - 1) = (-1/2) * x^(-3/2)

3. Simplify the expression: y' = (-1/2) / x^(3/2) = -1 / (2 * √x^3)

Therefore, the derivative of y = 1/√x is y' = -1 / (2 * √x^3).