What is (\partial)/(\partial x)(x^2-y^2+5xy) ?

The answer to (\partial)/(\partial x)(x^2-y^2+5xy) is 2x+5y

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(\partial)/(\partial x)(x^2-y^2+5xy)

\frac{\partial}{\partial x} (x^{2} - y^{2} + 5 x y)

2 x + 5 y

Solution steps

\frac{\partial}{\partial x} (x^{2} - y^{2} + 5 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (5 x y)

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

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

\frac{\partial}{\partial x} (5 x y) = 5 y

= 2 x - 0 + 5 y

Simplify

= 2 x + 5 y

f (x) = 2 - x

y^{^{''}} - 4 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 9

x \to 1 - lim (\frac{x}{( x - 1 ) ^{2}})

\frac{d y}{d x} = \frac{3 x + 2}{y}

\int \frac{3}{y ^{2}} d y

What is (\partial)/(\partial x)(x^2-y^2+5xy) ?
The answer to (\partial)/(\partial x)(x^2-y^2+5xy) is 2x+5y