What is the derivative of 9/x ?

The derivative of 9/x is -9/(x^2)

What is the first derivative of 9/x ?

The first derivative of 9/x is -9/(x^2)

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derivative of

\frac{9}{x}

- \frac{9}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{9}{x})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= 9 \frac{d}{d x} (x^{- 1})

Apply the Power Rule:

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

= 9 (- 1 \cdot x^{- 1 - 1})

Simplify

9 (- 1 \cdot x^{- 1 - 1}) : - \frac{9}{x ^{2}}

= - \frac{9}{x ^{2}}

x \to 0 - lim (3^{\frac{1}{x}})

\int \frac{x ^{2}}{x x ^{2} - x + 1} d x

\int x cos (\frac{1}{2} x) d x

y^{^{''}} + 3 y^{^{'}} + 2 y = x + 6 e^{x}, y (0) = 0, y^{^{'}} (0) = 1

y = sin (x y) + π, (1, π)