What is (\partial)/(\partial x)(ax+by) ?

The answer to (\partial)/(\partial x)(ax+by) is a

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(\partial)/(\partial x)(ax+by)

\frac{\partial}{\partial x} (a x + b y)

a

Solution steps

\frac{\partial}{\partial x} (a x + b y)

Treat

a, b, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (a x) + \frac{\partial}{\partial x} (b y)

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

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

= a + 0

Simplify

= a

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

\int 3 x cos (x^{2}) d x

\int \frac{1}{t ^{2} - 2 t + 17} d t

\frac{\partial}{\partial x} (7 x y - 3 x^{2} y)

x^{4} - 20 x^{2} + 64, at x = 2

What is (\partial)/(\partial x)(ax+by) ?
The answer to (\partial)/(\partial x)(ax+by) is a