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

The answer to (\partial)/(\partial x)(sin(x-y)+(x+y)) is cos(x-y)+1

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(\partial)/(\partial x)(sin(x-y)+(x+y))

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

cos (x - y) + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= cos (x - y) + 1 + 0

Simplify

= cos (x - y) + 1

\frac{\partial}{\partial x} (4 x + 2 y)

f (x) = 5 tan (x), (\frac{π}{4}, 5)

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

\int \frac{63}{1 - cos ( 7 x )} d x

\int e^{- 5 x} cos (x) d x

What is (\partial)/(\partial x)(sin(x-y)+(x+y)) ?
The answer to (\partial)/(\partial x)(sin(x-y)+(x+y)) is cos(x-y)+1