What is (\partial)/(\partial x)(e^tcos(x)) ?

The answer to (\partial)/(\partial x)(e^tcos(x)) is -e^tsin(x)

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(\partial)/(\partial x)(e^tcos(x))

\frac{\partial}{\partial x} (e^{t} cos (x))

- e^{t} sin (x)

Solution steps

\frac{\partial}{\partial x} (e^{t} cos (x))

Treat

t

as a constant

Take the constant out:

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

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

Apply the common derivative:

\frac{\partial}{\partial x} (cos (x)) = - sin (x)

= e^{t} (- sin (x))

Simplify

= - e^{t} sin (x)

What is (\partial)/(\partial x)(e^tcos(x)) ?
The answer to (\partial)/(\partial x)(e^tcos(x)) is -e^tsin(x)