Question

Найти производную 3/(√x^3) с решением

Answer 1

Ответ:

Производная равна:

$\displaystyle (3x^{-\frac{3}{2} })'=-\frac{9}{2\sqrt{x^5} }$

Пошаговое объяснение:

Требуется найти производную: 3/(√x^3)

Преобразуем выражение:

$\displaystyle \frac{3}{\sqrt{x^3} }=\frac{3}{x^{\frac{3}{2} }} =3x^{-\frac{3}{2} }$

Теперь найдем производную по формуле:

$\displaystyle \boxed {(x^n)'=nx^{n-1}}$

$\displaystyle (3x^{-\frac{3}{2} })'=3\cdot \left(-\frac{3}{2}\right)\cdot x^{-\frac{3}{2}-1 } =-\frac{9}{2}x^{-\frac{5}{2} }=-\frac{9}{2x^{\frac{5}{2} }} =-\frac{9}{2\sqrt{x^5} }$

Производная найдена.

Answer 2

Ответ:

$-\frac{9}{2*\sqrt{x}*|x| }$

Пошаговое объяснение:

y'=-3*$\frac{\frac{1}{2\sqrt{x^{3} } } 3x^{2} }{\sqrt{x^{3} } ^{2}}$=$-\frac{9}{2*\sqrt{x}*|x| }$

Answer 3

Finding the Derivative of 3/(√x^3)

To find the derivative of the function 3/(√x^3), we can use the power rule and chain rule of differentiation.

The given function can be rewritten as 3x^(-3/2). Applying the power rule, the derivative of the function is:

d/dx (3x^(-3/2))

Using the power rule, the derivative of x^n is n*x^(n-1). Therefore, the derivative of 3x^(-3/2) is:

= -3/2 * 3x^(-5/2)

Now, let's simplify this expression.

Simplifying the Derivative

Simplifying the expression -3/2 * 3x^(-5/2), we get:

= -9/(2x^(5/2))

So, the derivative of the function 3/(√x^3) is -9/(2x^(5/2)).

This is the final result for the derivative of the given function.