What is (\partial)/(\partial x)(x^2+2y^2+7z^2) ?

The answer to (\partial)/(\partial x)(x^2+2y^2+7z^2) is 2x

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(\partial)/(\partial x)(x^2+2y^2+7z^2)

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 7 z^{2})

2 x

Solution steps

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 7 z^{2})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (2 y^{2}) + \frac{\partial}{\partial x} (7 z^{2})

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

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

\frac{\partial}{\partial x} (7 z^{2}) = 0

= 2 x + 0 + 0

Simplify

= 2 x

\int \frac{1}{16 + 9 x ^{2}} d x

\frac{17}{x}

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

y^{^{''}} + 3 (y^{^{'}})^{2} = - 17

\int - 3 e^{- 3 x} d x

What is (\partial)/(\partial x)(x^2+2y^2+7z^2) ?
The answer to (\partial)/(\partial x)(x^2+2y^2+7z^2) is 2x