What is the d/(dy)(1/(xy)) ?

The d/(dy)(1/(xy)) is -1/(xy^2)

What is the first d/(dy)(1/(xy)) ?

The first d/(dy)(1/(xy)) is -1/(xy^2)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{6 t ^{3} - t ^{2} + 24 t}{t ^{2} + 4} d t

- \frac{5 s}{( ( s + 1 ) ^{2} + 3 )}

\frac{d}{d x} (e^{x^{3}} y)

\int 10 x^{\frac{3}{2}} + 6 x - 8 d x

\int \frac{5}{x} + sec^{2} (x) d x