What is the derivative of A/x ?

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

What is the first derivative of A/x ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

x \to 1 lim (x^{2} + 2 x - \frac{5}{2})

(x^{2} + 1) \frac{d y}{d x} + 4 x (y - 1) = 0, y (0) = 8

\int_{- 1}^{1} e^{y} - (y^{2} - 7) d y

\frac{d}{d x} (lo g_{9} (- (x - 4) (5 x - 2)))

\frac{\partial}{\partial y} (sin (x) y)