What is (\partial)/(\partial x)(e^{yx}*sin(2xy)) ?

The answer to (\partial)/(\partial x)(e^{yx}*sin(2xy)) is e^{yx}ysin(2xy)+cos(2xy)*2ye^{yx}

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(\partial)/(\partial x)(e^{yx}*sin(2xy))

\frac{\partial}{\partial x} (e^{y x} \cdot sin (2 x y))

e^{y x} y sin (2 x y) + cos (2 x y) \cdot 2 y e^{y x}

Solution steps

\frac{\partial}{\partial x} (e^{y x} sin (2 x y))

Treat

y

as a constant

Apply the Product Rule:

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

f = e^{y x}, g = sin (2 x y)

= \frac{\partial}{\partial x} (e^{y x}) sin (2 x y) + \frac{\partial}{\partial x} (sin (2 x y)) e^{y x}

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

\frac{\partial}{\partial x} (sin (2 x y)) = cos (2 x y) \cdot 2 y

= e^{y x} y sin (2 x y) + cos (2 x y) \cdot 2 y e^{y x}

\int_{- \infty}^{0} 9^{r} d r

\int sin (x) + 36 - x^{2} d x

\frac{d}{d x} (\frac{6 x}{x + 3})

x^{6} + y^{5} x^{7} + 2 y^{^{'}} = 0

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

What is (\partial)/(\partial x)(e^{yx}*sin(2xy)) ?
The answer to (\partial)/(\partial x)(e^{yx}*sin(2xy)) is e^{yx}ysin(2xy)+cos(2xy)*2ye^{yx}