What is the derivative of-(3x+1/(x^2)) ?

The derivative of-(3x+1/(x^2)) is -(-3x-2)/(x^3)

What is the first derivative of-(3x+1/(x^2)) ?

The first derivative of-(3x+1/(x^2)) is -(-3x-2)/(x^3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Cancel

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

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

4 (5 - 7 x)^{5}

x \cdot sin (π x)

\int - 3 e^{x} d x

\int (tan (x) + cot (x))^{2} d x

\int - 5 sin (3 x) d x

What is the derivative of-(3x+1/(x^2)) ?
The derivative of-(3x+1/(x^2)) is -(-3x-2)/(x^3)
What is the first derivative of-(3x+1/(x^2)) ?
The first derivative of-(3x+1/(x^2)) is -(-3x-2)/(x^3)