What is the d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y}) ?

The d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y}) is 2{x}+{y}

What is the first d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y}) ?

The first d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y}) is 2{x}+{y}

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\frac{d}{d x} (x^{2} + y^{2} + z^{2} + x y)

2 x + y

Solution steps

\frac{d}{d x} (x^{2} + y^{2} + z^{2} + x y)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (y^{2}) + \frac{d}{d x} (z^{2}) + \frac{d}{d x} (x y)

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (y^{2}) = 0

\frac{d}{d x} (z^{2}) = 0

\frac{d}{d x} (x y) = y

= 2 x + 0 + 0 + y

Simplify

= 2 x + y

x y^{2} + 3 y^{2} - x^{2} y^{^{'}} = 0

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

\int \frac{1}{t ^{\frac{3}{2}}} d t

\int \frac{2}{1 + 4 x ^{2}} d x

\int sin (\frac{1}{2})

What is the d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y}) ?
The d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y}) is 2{x}+{y}
What is the first d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y}) ?
The first d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y}) is 2{x}+{y}