What is (\partial)/(\partial x)(5cos(2x+5y)) ?

The answer to (\partial)/(\partial x)(5cos(2x+5y)) is -10sin(2x+5y)

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(\partial)/(\partial x)(5cos(2x+5y))

\frac{\partial}{\partial x} (5 cos (2 x + 5 y))

- 10 sin (2 x + 5 y)

Solution steps

\frac{\partial}{\partial x} (5 cos (2 x + 5 y))

Treat

y

as a constant

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (cos (2 x + 5 y))

Apply the chain rule:

- sin (2 x + 5 y) \frac{\partial}{\partial x} (2 x + 5 y)

= - sin (2 x + 5 y) \frac{\partial}{\partial x} (2 x + 5 y)

\frac{\partial}{\partial x} (2 x + 5 y) = 2

= 5 (- sin (2 x + 5 y) \cdot 2)

Simplify

= - 10 sin (2 x + 5 y)

\int \frac{5 x ^{3}}{6 + x ^{2}} d x

\frac{d}{d x} (2 sin (2 x))

\frac{d ^{4}}{d x ^{4}} (\frac{1}{x ^{2}})

\int x^{2} cos (mπ x) d x

sin (5 x) + cos (4 x)

What is (\partial)/(\partial x)(5cos(2x+5y)) ?
The answer to (\partial)/(\partial x)(5cos(2x+5y)) is -10sin(2x+5y)