What is (\partial)/(\partial x)(cos(x+5y)) ?

The answer to (\partial)/(\partial x)(cos(x+5y)) is -sin(x+5y)

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(\partial)/(\partial x)(cos(x+5y))

\frac{\partial}{\partial x} (cos (x + 5 y))

- sin (x + 5 y)

Solution steps

\frac{\partial}{\partial x} (cos (x + 5 y))

Treat

y

as a constant

Apply the chain rule:

- sin (x + 5 y) \frac{\partial}{\partial x} (x + 5 y)

= - sin (x + 5 y) \frac{\partial}{\partial x} (x + 5 y)

\frac{\partial}{\partial x} (x + 5 y) = 1

= - sin (x + 5 y) \cdot 1

Simplify

= - sin (x + 5 y)

(2 x + 5) (- x + 2)

\int \frac{4 x ^{3} - x}{6 x ^{2} - 2 x - 1} d x

x \to 0 lim (\frac{( 3 x ^{2} - 2 x )}{x})

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

\int \frac{x ^{3}}{x ^{2} - 16} d x

What is (\partial)/(\partial x)(cos(x+5y)) ?
The answer to (\partial)/(\partial x)(cos(x+5y)) is -sin(x+5y)