What is (\partial)/(\partial x)(3x^2+2xy+y^2-11) ?

The answer to (\partial)/(\partial x)(3x^2+2xy+y^2-11) is 6x+2y

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(\partial)/(\partial x)(3x^2+2xy+y^2-11)

\frac{\partial}{\partial x} (3 x^{2} + 2 x y + y^{2} - 11)

6 x + 2 y

Solution steps

\frac{\partial}{\partial x} (3 x^{2} + 2 x y + y^{2} - 11)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (2 x y) + \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (11)

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

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

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

\frac{\partial}{\partial x} (11) = 0

= 6 x + 2 y + 0 - 0

Simplify

= 6 x + 2 y

15 t^{3}

f (x) = sin (x cos (x))

t \frac{d y}{d t} + 2 y = sin (t)

\int_{0}^{3} (e^{x}) d x

\int (4 x^{3} + 5 x) e^{x^{2}} d x

What is (\partial)/(\partial x)(3x^2+2xy+y^2-11) ?
The answer to (\partial)/(\partial x)(3x^2+2xy+y^2-11) is 6x+2y