What is (\partial)/(\partial x)(8ye^x-ln(z)) ?

The answer to (\partial)/(\partial x)(8ye^x-ln(z)) is 8e^xy

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(\partial)/(\partial x)(8ye^x-ln(z))

\frac{\partial}{\partial x} (8 y e^{x} - ln (z))

8 e^{x} y

Solution steps

\frac{\partial}{\partial x} (8 y e^{x} - ln (z))

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (8 y e^{x}) - \frac{\partial}{\partial x} (ln (z))

\frac{\partial}{\partial x} (8 y e^{x}) = 8 y e^{x}

\frac{\partial}{\partial x} (ln (z)) = 0

= 8 y e^{x} - 0

Simplify

= 8 e^{x} y

\frac{( s + 1 ) ^{3}}{s ^{6}}

\int \frac{1}{( 3 + y ) ^{5}} d y

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

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

\frac{d}{d x} (sin^{e^{x}} (x))

What is (\partial)/(\partial x)(8ye^x-ln(z)) ?
The answer to (\partial)/(\partial x)(8ye^x-ln(z)) is 8e^xy