What is (\partial)/(\partial x)(20+5sin(x)cos(x-y)) ?

The answer to (\partial)/(\partial x)(20+5sin(x)cos(x-y)) is 5cos(2x-y)

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(\partial)/(\partial x)(20+5sin(x)cos(x-y))

\frac{\partial}{\partial x} (20 + 5 sin (x) cos (x - y))

5 cos (2 x - y)

Solution steps

\frac{\partial}{\partial x} (20 + 5 sin (x) cos (x - y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (20) + \frac{\partial}{\partial x} (5 sin (x) cos (x - y))

\frac{\partial}{\partial x} (20) = 0

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

= 0 + 5 cos (2 x - y)

Simplify

= 5 cos (2 x - y)

\int \frac{e ^{2 x}}{x} d x

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

\int sin (3 x) sin (7 x) d x

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

x \to 1 lim (\frac{x ^{3} + 1}{x + 1})

What is (\partial)/(\partial x)(20+5sin(x)cos(x-y)) ?
The answer to (\partial)/(\partial x)(20+5sin(x)cos(x-y)) is 5cos(2x-y)