What is the derivative of (a^1)/x ?

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

What is the first derivative of (a^1)/x ?

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

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derivative of

\frac{a ^{1}}{x}

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

Solution steps

\frac{d}{d x} (\frac{a ^{1}}{x})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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

ln ((2 x + 1)^{2})

(x - 2) (x + 2)^{3}

y = sin (x^{2} + 2)

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

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