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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

\frac{8}{x x ^{2} - 4}

x \to \infty lim ((k)^{x})

x \to 1 lim (tan (x))

y^{^{'}} = \frac{( x ^{4} y ^{4} + 4 x ^{4} )}{y ^{3}}

y^{^{''}} - 3 y^{^{'}} - 4 y = - 8 e^{t} cos (2 t)

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