What is (\partial)/(\partial x)(cos(x+4y)) ?

The answer to (\partial)/(\partial x)(cos(x+4y)) is -sin(x+4y)

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(\partial)/(\partial x)(cos(x+4y))

\frac{\partial}{\partial x} (cos (x + 4 y))

- sin (x + 4 y)

Solution steps

\frac{\partial}{\partial x} (cos (x + 4 y))

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x + 4 y) = 1

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

Simplify

= - sin (x + 4 y)

200 + \frac{7}{x} + \frac{x ^{2}}{7}

\int \frac{- 4 x + 1}{x ^{2} + 2} d x

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

\frac{d}{d x} (- 4 sin (4 x))

y = x - 1, y = - x + 3, x

What is (\partial)/(\partial x)(cos(x+4y)) ?
The answer to (\partial)/(\partial x)(cos(x+4y)) is -sin(x+4y)