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

m = 1 \sum \infty 3 \cdot (\frac{1}{3})

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

\int 8 tan (8 x) d x

x \to 9 lim (25 - x)

t an g e n t f (x) = 3 x^{2} - 10 x

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