Question

F'(x)=5x√x найти F(x)

Answer 1

F'=5x^3/2 F=5/(3/2+1)x^(3/2+1)=5*2/5x^5/2=2x^(5/2)

Answer 2

To find the function F(x), given that its derivative F'(x) is equal to 5x√x, we can integrate F'(x) with respect to x. Integrating F'(x) will give us F(x) up to a constant of integration.

Let's break down the problem step by step:

Step 1: Start with the derivative F'(x) = 5x√x.

Step 2: To integrate 5x√x with respect to x, we can use the power rule for integration, which states that ∫x^n dx = (x^(n+1))/(n+1), where n is any real number except -1.

In this case, we have x as the base and √x as the exponent. Using the power rule, we can rewrite the expression as:

∫5x√x dx = 5∫(x^(3/2)) dx.

Step 3: Applying the power rule, we increase the exponent by 1 and divide by the new exponent:

= 5 * (2/5) * x^(5/2) + C, where C is the constant of integration.

Simplifying further, we get:

= 2x^(5/2) + C.

Therefore, the function F(x) = 2x^(5/2) + C, where C is an arbitrary constant.

That's the detailed solution for finding F(x) given F'(x) = 5x√x.