What is (\partial)/(\partial x)(x^{2+2y^2+3z^2}) ?

The answer to (\partial)/(\partial x)(x^{2+2y^2+3z^2}) is x^{2y^2+3z^2+1}(2+2y^2+3z^2)

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(\partial)/(\partial x)(x^{2+2y^2+3z^2})

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

x^{2 y^{2} + 3 z^{2} + 1} (2 + 2 y^{2} + 3 z^{2})

Solution steps

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

Treat

y, z

as constants

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= (2 + 2 y^{2} + 3 z^{2}) x^{2 + 2 y^{2} + 3 z^{2} - 1}

Simplify

= x^{2 y^{2} + 3 z^{2} + 1} (2 + 2 y^{2} + 3 z^{2})

\frac{d}{d x} (2 x^{4 π})

\int \frac{x + 4}{x ^{3} + x ^{2} - 2} d x

\frac{d}{d y} (x^{y^{z}})

f (x) = \frac{5}{1 - 9 x}

f (x) = 6 e^{x} + 4 x^{2}

What is (\partial)/(\partial x)(x^{2+2y^2+3z^2}) ?
The answer to (\partial)/(\partial x)(x^{2+2y^2+3z^2}) is x^{2y^2+3z^2+1}(2+2y^2+3z^2)