What is the derivative of n/x ?

The derivative of n/x is -n/(x^2)

What is the first derivative of n/x ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= n \frac{d}{d x} (x^{- 1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= n (- 1 \cdot x^{- 1 - 1})

Simplify

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

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

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

f^{^{'}} (t) - f (t) = - 8 t

\int e^{i 6 x} cos (4 x) d x

\int 1 + (- tan (x))^{2} d x

\frac{\partial}{\partial v} (\frac{v}{u})