What is (\partial)/(\partial x)(2x^2+y^2-9y) ?

The answer to (\partial)/(\partial x)(2x^2+y^2-9y) is 4x

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(\partial)/(\partial x)(2x^2+y^2-9y)

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

4 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

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

\frac{\partial}{\partial x} (9 y) = 0

= 4 x + 0 - 0

Simplify

= 4 x

2 y^{^{''}} + 7 y^{^{'}} + 5 y = 0

\int_{3}^{5} (- x^{2} + 8 x - 12) d x

x \to 2 lim (3 x + 6)

\int (x^{2} + 1) (x^{3} + 3 x) d x

\frac{d}{d x} (8 e^{2})

What is (\partial)/(\partial x)(2x^2+y^2-9y) ?
The answer to (\partial)/(\partial x)(2x^2+y^2-9y) is 4x