What is (\partial)/(\partial x)(8sin(xy)) ?

The answer to (\partial)/(\partial x)(8sin(xy)) is 8cos(xy)y

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(\partial)/(\partial x)(8sin(xy))

\frac{\partial}{\partial x} (8 sin (x y))

8 cos (x y) y

Solution steps

\frac{\partial}{\partial x} (8 sin (x y))

Treat

y

as a constant

Take the constant out:

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

= 8 \frac{\partial}{\partial x} (sin (x y))

Apply the chain rule:

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

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

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

= 8 cos (x y) y

\frac{d}{d y} (\frac{1}{4 y ^{2}})

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

2 y \frac{d y}{d x} = x (y^{2} + 1)

cos (x) d y + (y sin (x) - cos^{4} (x)) d x = 0

f (x) = x + 2 sin (x)

What is (\partial)/(\partial x)(8sin(xy)) ?
The answer to (\partial)/(\partial x)(8sin(xy)) is 8cos(xy)y