What is (\partial)/(\partial x)(cos(x+3y)) ?

The answer to (\partial)/(\partial x)(cos(x+3y)) is -sin(x+3y)

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(\partial)/(\partial x)(cos(x+3y))

\frac{\partial}{\partial x} (cos (x + 3 y))

- sin (x + 3 y)

Solution steps

\frac{\partial}{\partial x} (cos (x + 3 y))

Treat

y

as a constant

Apply the chain rule:

- sin (x + 3 y) \frac{\partial}{\partial x} (x + 3 y)

= - sin (x + 3 y) \frac{\partial}{\partial x} (x + 3 y)

\frac{\partial}{\partial x} (x + 3 y) = 1

= - sin (x + 3 y) \cdot 1

Simplify

= - sin (x + 3 y)

\frac{d}{d x} (3 x^{2} - 2 x - 1)

\frac{d}{d x} (1 - \frac{2}{x})

\int 4 - 2 x^{2} d x

x \to 2.99 lim (x^{2} + 3 x)

e^{8}

What is (\partial)/(\partial x)(cos(x+3y)) ?
The answer to (\partial)/(\partial x)(cos(x+3y)) is -sin(x+3y)