What is (\partial)/(\partial x)(2cos(x+2y)) ?

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

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(\partial)/(\partial x)(2cos(x+2y))

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

- 2 sin (x + 2 y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 2 (- sin (x + 2 y) \cdot 1)

Simplify

= - 2 sin (x + 2 y)

x^{2} sin^{4} (x) + x cos^{- 2} (x)

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

\frac{\partial}{\partial x} (4 y^{3} cos (3 x))

h (x) = e^{x}

x \to \infty lim (1 + 2 x)

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