What is the derivative of ln(xy) ?

The derivative of ln(xy) is 1/x

What is the first derivative of ln(xy) ?

The first derivative of ln(xy) is 1/x

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derivative of

ln (x y)

\frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{x y} y

Simplify

\frac{1}{x y} y : \frac{1}{x}

= \frac{1}{x}

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = - 11

x^{6} + y^{5} x^{7} + 5 y^{^{'}} = 0

\int e^{- t x} sin (x) d x

x \to - 1 lim (3 x^{2} - 1)

\int \frac{1}{e ^{2 x}} d x