What is the derivative of (5sqrt(x)/(x^3)) ?

The derivative of (5sqrt(x)/(x^3)) is -(25)/(2x^{7/2)}

What is the first derivative of (5sqrt(x)/(x^3)) ?

The first derivative of (5sqrt(x)/(x^3)) is -(25)/(2x^{7/2)}

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\frac{d}{d x} (\frac{5 x}{x ^{3}})

- \frac{25}{2 x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{5 x}{x ^{3}})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{x}{x ^{3}})

Apply the Quotient Rule:

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

= 5 \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}

= 5 \cdot \frac{\frac{1}{2 x} x ^{3} - 3 x ^{2} x}{( x ^{3} ) ^{2}}

Simplify

5 \cdot \frac{\frac{1}{2 x} x ^{3} - 3 x ^{2} x}{( x ^{3} ) ^{2}} : - \frac{25}{2 x ^{\frac{7}{2}}}

= - \frac{25}{2 x ^{\frac{7}{2}}}

(x, y) \to (0, 2) lim (x^{3} y)

x - 84

\frac{d}{d x} (40 x)

\int x sec^{2} (8 x) d x

x \to 0 lim ((1 - (x))^{\frac{1}{x}})

What is the derivative of (5sqrt(x)/(x^3)) ?
The derivative of (5sqrt(x)/(x^3)) is -(25)/(2x^{7/2)}
What is the first derivative of (5sqrt(x)/(x^3)) ?
The first derivative of (5sqrt(x)/(x^3)) is -(25)/(2x^{7/2)}