What is the derivative of (d/(dx(sqrt(x)))^2) ?

The derivative of (d/(dx(sqrt(x)))^2) is -1/(4x^2)

What is the first derivative of (d/(dx(sqrt(x)))^2) ?

The first derivative of (d/(dx(sqrt(x)))^2) is -1/(4x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} ((\frac{d}{d x} (x))^{2})

- \frac{1}{4 x ^{2}}

Solution steps

\frac{d}{d x} ((\frac{d}{d x} (x))^{2})

Apply the chain rule:

2 \frac{d}{d x} (x) \frac{d}{d x} (\frac{d}{d x} (x))

= 2 \frac{d}{d x} (x) \frac{d}{d x} (\frac{d}{d x} (x))

\frac{d}{d x} (\frac{d}{d x} (x)) = - \frac{1}{4 x ^{\frac{3}{2}}}

= 2 \frac{d}{d x} (x) (- \frac{1}{4 x ^{\frac{3}{2}}})

Apply radical rule:

a = a^{\frac{1}{2}}

= 2 \frac{d}{d x} (x^{\frac{1}{2}}) (- \frac{1}{4 x ^{\frac{3}{2}}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} (- \frac{1}{4 x ^{\frac{3}{2}}})

Simplify

2 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} (- \frac{1}{4 x ^{\frac{3}{2}}}) : - \frac{1}{4 x ^{2}}

= - \frac{1}{4 x ^{2}}

\frac{d y}{d x} = 2 x e^{2 y}

\frac{d}{d x} (2 arctan (\frac{y}{x}))

\int \frac{2 x - 1}{x} d x

d er i v a t i v e x^{2} sin (4 x)

\frac{\partial}{\partial x} (6 x^{5} y^{6} + 8 x^{7} y^{8})

What is the derivative of (d/(dx(sqrt(x)))^2) ?
The derivative of (d/(dx(sqrt(x)))^2) is -1/(4x^2)
What is the first derivative of (d/(dx(sqrt(x)))^2) ?
The first derivative of (d/(dx(sqrt(x)))^2) is -1/(4x^2)