What is (\partial)/(\partial x)(ln(x/(y-z))) ?

The answer to (\partial)/(\partial x)(ln(x/(y-z))) is 1/x

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(\partial)/(\partial x)(ln(x/(y-z)))

\frac{\partial}{\partial x} (ln (\frac{x}{y - z}))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{x}{y - z}))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{\frac{x}{y - z}} \frac{\partial}{\partial x} (\frac{x}{y - z})

= \frac{1}{\frac{x}{y - z}} \frac{\partial}{\partial x} (\frac{x}{y - z})

\frac{\partial}{\partial x} (\frac{x}{y - z}) = \frac{1}{y - z}

= \frac{1}{\frac{x}{y - z}} \cdot \frac{1}{y - z}

Simplify

\frac{1}{\frac{x}{y - z}} \cdot \frac{1}{y - z} : \frac{1}{x}

= \frac{1}{x}

\frac{\partial}{\partial y} (y^{2} cos (y))

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

f (x) = (x^{3} + 5) e^{x}

\int_{- \infty}^{0} e^{- 2 x} d x

y^{^{''}} + 10 y^{^{'}} + 21 y = 0

What is (\partial)/(\partial x)(ln(x/(y-z))) ?
The answer to (\partial)/(\partial x)(ln(x/(y-z))) is 1/x