What is (\partial)/(\partial x)(1/2 sin(2x-y)) ?

The answer to (\partial)/(\partial x)(1/2 sin(2x-y)) is cos(2x-y)

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(\partial)/(\partial x)(1/2 sin(2x-y))

\frac{\partial}{\partial x} (\frac{1}{2} sin (2 x - y))

cos (2 x - y)

Solution steps

\frac{\partial}{\partial x} (\frac{1}{2} sin (2 x - y))

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{2} \frac{\partial}{\partial x} (sin (2 x - y))

Apply the chain rule:

cos (2 x - y) \frac{\partial}{\partial x} (2 x - y)

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

\frac{\partial}{\partial x} (2 x - y) = 2

= \frac{1}{2} cos (2 x - y) \cdot 2

Simplify

\frac{1}{2} cos (2 x - y) \cdot 2 : cos (2 x - y)

= cos (2 x - y)

\frac{\partial}{\partial x} (\frac{x ^{3} b ^{4}}{c ^{2} d ^{4}})

y = 4 x, x = 0, y = 4

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

x \to 0 lim (4 - x)

\frac{d}{d x} (- 2 9 x^{2} + 8)

What is (\partial)/(\partial x)(1/2 sin(2x-y)) ?
The answer to (\partial)/(\partial x)(1/2 sin(2x-y)) is cos(2x-y)