What is (\partial)/(\partial x)(1/2 (x-y)^2) ?

The answer to (\partial)/(\partial x)(1/2 (x-y)^2) is x-y

Popular >

(\partial)/(\partial x)(1/2 (x-y)^2)

\frac{\partial}{\partial x} (\frac{1}{2} (x - y)^{2})

x - y

Solution steps

\frac{\partial}{\partial x} (\frac{1}{2} (x - y)^{2})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{2} \frac{\partial}{\partial x} ((x - y)^{2})

Apply the chain rule:

2 (x - y) \frac{\partial}{\partial x} (x - y)

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

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

= \frac{1}{2} \cdot 2 (x - y) \cdot 1

Simplify

\frac{1}{2} \cdot 2 (x - y) \cdot 1 : x - y

= x - y

t y^{^{'}} + 2 y = 4 t^{2}

x \to - 2 lim (\frac{x}{x ^{2} - 4})

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

\int \frac{5}{32} x^{4} d x

x sin (\frac{1}{x})

What is (\partial)/(\partial x)(1/2 (x-y)^2) ?
The answer to (\partial)/(\partial x)(1/2 (x-y)^2) is x-y