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

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

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(\partial)/(\partial x)(e^xsin(xy))

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

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

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

\frac{\partial}{\partial x} (x + y + z)

\frac{\partial}{\partial x} ((4 x - y^{2})^{\frac{3}{2}})

n = 1 \sum \infty \frac{6}{2 ^{n}}

\frac{\partial}{\partial x} (y (1 - x))

e^{- 3 s} \cdot \frac{5}{4 s ^{2} + 16}

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