What is (\partial)/(\partial x)(a(x-b)) ?

The answer to (\partial)/(\partial x)(a(x-b)) is a

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(\partial)/(\partial x)(a(x-b))

\frac{\partial}{\partial x} (a (x - b))

a

Solution steps

\frac{\partial}{\partial x} (a (x - b))

Treat

a, b

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= a (1 - 0)

Simplify

= a

\int \frac{2 x + 5}{x} d x

\int_{0}^{16} x 16 - x d x

\int_{0}^{\infty} \frac{x}{x ^{3} + 1} d x

x \to 3 lim (\frac{4 x - 5}{5 x - 1})

\int + x^{2} x^{3} + 27 d x

What is (\partial)/(\partial x)(a(x-b)) ?
The answer to (\partial)/(\partial x)(a(x-b)) is a