What is (\partial)/(\partial x)(5ye^x-ln(z)) ?

The answer to (\partial)/(\partial x)(5ye^x-ln(z)) is 5e^xy

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(\partial)/(\partial x)(5ye^x-ln(z))

\frac{\partial}{\partial x} (5 y e^{x} - ln (z))

5 e^{x} y

Solution steps

\frac{\partial}{\partial x} (5 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} (5 y e^{x}) - \frac{\partial}{\partial x} (ln (z))

\frac{\partial}{\partial x} (5 y e^{x}) = 5 y e^{x}

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

= 5 y e^{x} - 0

Simplify

= 5 e^{x} y

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e^{- 2 t} cos (3 t)

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What is (\partial)/(\partial x)(5ye^x-ln(z)) ?
The answer to (\partial)/(\partial x)(5ye^x-ln(z)) is 5e^xy