What is (\partial)/(\partial x)(7ln((2xy)/(5z))) ?

The answer to (\partial)/(\partial x)(7ln((2xy)/(5z))) is 7/x

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(\partial)/(\partial x)(7ln((2xy)/(5z)))

\frac{\partial}{\partial x} (7 ln (\frac{2 x y}{5 z}))

\frac{7}{x}

Solution steps

\frac{\partial}{\partial x} (7 ln (\frac{2 x y}{5 z}))

Treat

y, z

as constants

Take the constant out:

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

= 7 \frac{\partial}{\partial x} (ln (\frac{2 x y}{5 z}))

Apply the chain rule:

\frac{1}{\frac{2 x y}{5 z}} \frac{\partial}{\partial x} (\frac{2 x y}{5 z})

= \frac{1}{\frac{2 x y}{5 z}} \frac{\partial}{\partial x} (\frac{2 x y}{5 z})

\frac{\partial}{\partial x} (\frac{2 x y}{5 z}) = \frac{2 y}{5 z}

= 7 \cdot \frac{1}{\frac{2 x y}{5 z}} \cdot \frac{2 y}{5 z}

Simplify

7 \cdot \frac{1}{\frac{2 x y}{5 z}} \cdot \frac{2 y}{5 z} : \frac{7}{x}

= \frac{7}{x}

\frac{\partial ^{2}}{\partial x ^{2}} (\frac{x}{x ^{2} + y ^{2}})

\int 2 x e^{7 x} d x

\int - 2 x + 9 x^{2} - 4 x^{3} + 14 d x

10 e^{x^{2}} x

\frac{\partial}{\partial x} ((x^{2} + y^{2} + z^{2})^{\frac{n}{2}})

What is (\partial)/(\partial x)(7ln((2xy)/(5z))) ?
The answer to (\partial)/(\partial x)(7ln((2xy)/(5z))) is 7/x