What is the derivative of (7sqrt(x)/(2x^3)) ?

The derivative of (7sqrt(x)/(2x^3)) is -(35)/(4x^{7/2)}

What is the first derivative of (7sqrt(x)/(2x^3)) ?

The first derivative of (7sqrt(x)/(2x^3)) is -(35)/(4x^{7/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{7 x}{2 x ^{3}})

- \frac{35}{4 x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{7 x}{2 x ^{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{7}{2} \frac{d}{d x} (\frac{x}{x ^{3}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{7}{2} \cdot \frac{\frac{d}{d x} ( x ) x ^{3} - \frac{d}{d x} ( x ^{3} ) x}{( x ^{3} ) ^{2}}

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{7}{2} \cdot \frac{\frac{1}{2 x} x ^{3} - 3 x ^{2} x}{( x ^{3} ) ^{2}}

Simplify

\frac{7}{2} \cdot \frac{\frac{1}{2 x} x ^{3} - 3 x ^{2} x}{( x ^{3} ) ^{2}} : - \frac{35}{4 x ^{\frac{7}{2}}}

= - \frac{35}{4 x ^{\frac{7}{2}}}

What is the derivative of (7sqrt(x)/(2x^3)) ?
The derivative of (7sqrt(x)/(2x^3)) is -(35)/(4x^{7/2)}
What is the first derivative of (7sqrt(x)/(2x^3)) ?
The first derivative of (7sqrt(x)/(2x^3)) is -(35)/(4x^{7/2)}