What is (\partial)/(\partial x)(6x^2+9xy+5y^2) ?

The answer to (\partial)/(\partial x)(6x^2+9xy+5y^2) is 12x+9y

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(\partial)/(\partial x)(6x^2+9xy+5y^2)

\frac{\partial}{\partial x} (6 x^{2} + 9 x y + 5 y^{2})

12 x + 9 y

Solution steps

\frac{\partial}{\partial x} (6 x^{2} + 9 x y + 5 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x^{2}) + \frac{\partial}{\partial x} (9 x y) + \frac{\partial}{\partial x} (5 y^{2})

\frac{\partial}{\partial x} (6 x^{2}) = 12 x

\frac{\partial}{\partial x} (9 x y) = 9 y

\frac{\partial}{\partial x} (5 y^{2}) = 0

= 12 x + 9 y + 0

Simplify

= 12 x + 9 y

((1 + sin (x))^{2} + (1 + cos (x))^{4})^{^{'}}

\int (x + 1) 2 d x

y^{^{'}} - 4 y = 2 x y^{2}

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

\frac{x}{x + 25}

What is (\partial)/(\partial x)(6x^2+9xy+5y^2) ?
The answer to (\partial)/(\partial x)(6x^2+9xy+5y^2) is 12x+9y