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

The answer to (\partial)/(\partial x)(5x^2+xy+2y^2) is 10x+y

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

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

10 x + y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

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

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

= 10 x + y + 0

Simplify

= 10 x + y

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

\frac{d}{d y} (\frac{y ^{3}}{39} + \frac{13}{4 y})

5 x^{4}

\frac{d}{d x} (x^{3} + 3 x y^{2} - 15 x - 12 y)

\frac{d}{d x} (ln (9 x^{2} - 7 x + 1))

What is (\partial)/(\partial x)(5x^2+xy+2y^2) ?
The answer to (\partial)/(\partial x)(5x^2+xy+2y^2) is 10x+y