What is the derivative of (x+3/x) ?

The derivative of (x+3/x) is -3/(x^2)

What is the first derivative of (x+3/x) ?

The first derivative of (x+3/x) is -3/(x^2)

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\frac{d}{d x} (\frac{x + 3}{x})

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

Solution steps

\frac{d}{d x} (\frac{x + 3}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 3) = 1

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

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

Simplify

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

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

3 x e^{- x}

\frac{d}{d x} (5^{(6 x^{2} - 7 x) (8 x^{2} + 9)})

\int - 2 x + 9 x^{2} - 4 x^{3} + 16 d x

\int e^{7 x} sin (3 x) d x

\int 8 tan^{3} (x) sec (x) d x

What is the derivative of (x+3/x) ?
The derivative of (x+3/x) is -3/(x^2)
What is the first derivative of (x+3/x) ?
The first derivative of (x+3/x) is -3/(x^2)