What is (\partial)/(\partial x)(e^xcos(x+y)) ?

The answer to (\partial)/(\partial x)(e^xcos(x+y)) is e^xcos(x+y)-e^xsin(x+y)

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(\partial)/(\partial x)(e^xcos(x+y))

\frac{\partial}{\partial x} (e^{x} cos (x + y))

e^{x} cos (x + y) - e^{x} sin (x + y)

Solution steps

\frac{\partial}{\partial x} (e^{x} cos (x + y))

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cos (x + y)

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

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

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

= e^{x} cos (x + y) + (- sin (x + y)) e^{x}

Simplify

= e^{x} cos (x + y) - e^{x} sin (x + y)

sec (\frac{π}{3})

\int sec^{4} (\frac{x}{4}) d x

\frac{d}{d x} (\frac{5}{( x - 6 ) ^{2}})

\int_{\frac{1}{5}}^{3} 8 x ln (5 x) d x

ln (e)

What is (\partial)/(\partial x)(e^xcos(x+y)) ?
The answer to (\partial)/(\partial x)(e^xcos(x+y)) is e^xcos(x+y)-e^xsin(x+y)