What is (\partial)/(\partial x)(e^xsin(10y+5z)) ?

The answer to (\partial)/(\partial x)(e^xsin(10y+5z)) is sin(10y+5z)e^x

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(\partial)/(\partial x)(e^xsin(10y+5z))

\frac{\partial}{\partial x} (e^{x} sin (10 y + 5 z))

sin (10 y + 5 z) e^{x}

Solution steps

\frac{\partial}{\partial x} (e^{x} sin (10 y + 5 z))

Treat

y, z

as constants

Take the constant out:

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

= sin (10 y + 5 z) \frac{\partial}{\partial x} (e^{x})

Apply the common derivative:

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

= sin (10 y + 5 z) e^{x}

What is (\partial)/(\partial x)(e^xsin(10y+5z)) ?
The answer to (\partial)/(\partial x)(e^xsin(10y+5z)) is sin(10y+5z)e^x