Question

Найти производную F(x)=x(1+√x)

Answer 1

Ответ на фото на фото ответ

Answer 2

I can help you find the derivative of F(x)=x(1+√x) using the product rule and the chain rule. Here are the steps:

- First, rewrite F(x) as F(x)=x(x^0.5) using the property that √x=x^0.5. - Next, apply the product rule to F(x), which states that (uv)'=u'v+uv'. Let u=x and v=x^0.5, then u'=1 and v'=0.5x^-0.5 by the chain rule. - Therefore, F'(x)=(x)'(x^0.5)+x(x^0.5)'=1(x^0.5)+x(0.5x^-0.5). - Simplify the expression by finding a common denominator and adding the fractions. F'(x)=(2x^0.5+0.5x^0)/x^0.5=(2.5x^0.5+0.5)/x^0.5. - Finally, rewrite F'(x) using the radical notation. F'(x)=(2.5√x+0.5)/√x.

This is the answer. You can also check some online calculators for more examples and explanations , , , . I hope this helps.