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

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

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

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

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\frac{d}{d x} (\frac{7 x}{x})

- \frac{7}{2 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{7 x}{x})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{x}{x})

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

7 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}} : - \frac{7}{2 x ^{\frac{3}{2}}}

= - \frac{7}{2 x ^{\frac{3}{2}}}

\frac{( a x + b )}{c x + d}

\int \frac{2 x - 3}{x ^{2} - 3 x + 1} d x

e^{x + 1}

\int 21 e^{x} d x

\int_{1}^{3} \frac{4}{x ^{2}} d x

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