What is the derivative of 1/(xy) ?

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

What is the first derivative of 1/(xy) ?

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

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derivative of

\frac{1}{x y}

- \frac{1}{x ^{2} y}

Solution steps

\frac{d}{d x} (\frac{1}{x y})

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{1}{x ^{2} y}

f^{^{'}} (θ) = θ cos (θ) sin (θ)

y^{^{''}} + 8 y^{^{'}} + 32 y = 128, y (0) = 0, y^{^{'}} (0) = 0

\frac{d}{d t} (x y (t) z (t))

y^{^{'}} + tan (x) y = \frac{1}{cos ( x )}

\int_{1}^{2} 3 x^{- 2} d x

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