What is (\partial)/(\partial x)(10-(3x^2+3y^2)) ?

The answer to (\partial)/(\partial x)(10-(3x^2+3y^2)) is -6x

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(\partial)/(\partial x)(10-(3x^2+3y^2))

\frac{\partial}{\partial x} (10 - (3 x^{2} + 3 y^{2}))

- 6 x

Solution steps

\frac{\partial}{\partial x} (10 - (3 x^{2} + 3 y^{2}))

Simplify

10 - (3 x^{2} + 3 y^{2}) : 10 - 3 x^{2} - 3 y^{2}

= \frac{\partial}{\partial x} (10 - 3 x^{2} - 3 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (10) - \frac{\partial}{\partial x} (3 x^{2}) - \frac{\partial}{\partial x} (3 y^{2})

\frac{\partial}{\partial x} (10) = 0

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 0 - 6 x - 0

Simplify

= - 6 x

\frac{d}{d x} (3 x^{2} - 4 x + 1)

\int \frac{3}{e ^{\frac{t}{2}}} d t

\int e^{x^{6}} d x

\int 6 x^{2} sin (x^{3}) d x

\int \frac{12}{x ^{2} x ^{2} + 16} d x

What is (\partial)/(\partial x)(10-(3x^2+3y^2)) ?
The answer to (\partial)/(\partial x)(10-(3x^2+3y^2)) is -6x