What is (\partial)/(\partial x)(4xsin(xy)) ?

The answer to (\partial)/(\partial x)(4xsin(xy)) is 4(sin(xy)+xycos(xy))

(\partial)/(\partial x)(4xsin(xy))

\frac{\partial}{\partial x} (4 x sin (x y))

4 (sin (x y) + x y cos (x y))

Solution steps

\frac{\partial}{\partial x} (4 x sin (x y))

Treat

y

as a constant

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (x sin (x y))

Apply the Product Rule:

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

f = x, g = sin (x y)

= 4 (\frac{\partial}{\partial x} (x) sin (x y) + \frac{\partial}{\partial x} (sin (x y)) x)

\frac{\partial}{\partial x} (x) = 1

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

= 4 (1 \cdot sin (x y) + cos (x y) y x)

Simplify

= 4 (sin (x y) + x y cos (x y))

\frac{\partial}{\partial x} (3 x^{2} + x y + y^{2} - 8)

\frac{d}{d x} (lo g_{e} (3 x))

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

y^{^{'}} + 8 y = 1, y (0) = 1

\frac{d}{d x} (\frac{x - 5}{4 x ^{2} e ^{x}})

What is (\partial)/(\partial x)(4xsin(xy)) ?
The answer to (\partial)/(\partial x)(4xsin(xy)) is 4(sin(xy)+xycos(xy))