Question

(x-1) √x производная ​

Answer 1

ответ на картинке

Объяснение:

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Answer 2

To find the derivative of the expression (x - 1)√x, we can apply the product rule and the chain rule. The product rule states that if we have two functions u(x) and v(x), the derivative of their product is given by:

(d/dx)(u(x)v(x)) = u(x)(d/dx)v(x) + v(x)(d/dx)u(x)

In this case, let's consider u(x) = x - 1 and v(x) = √x. We can differentiate each function separately using the power rule and the constant rule:

(d/dx)(x - 1) = 1 - 0 = 1

(d/dx)√x = (1/2)(x^(-1/2)) = 1/(2√x)

Now, we can substitute these derivatives into the product rule formula:

(d/dx)[(x - 1)√x] = (x - 1)(1/(2√x)) + √x(1)

Simplifying this expression, we have:

(d/dx)[(x - 1)√x] = (x - 1)/(2√x) + √x

This is the derivative of the expression (x - 1)√x.