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

The answer to (\partial)/(\partial x)(3x^{3y}) is 9yx^{3y-1}

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(\partial)/(\partial x)(3x^{3y})

\frac{\partial}{\partial x} (3 x^{3 y})

9 y x^{3 y - 1}

Solution steps

\frac{\partial}{\partial x} (3 x^{3 y})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

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

= 3 \cdot 3 y x^{3 y - 1}

Simplify

= 9 y x^{3 y - 1}

y^{^{''}} + y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 2

x \to \infty lim (e^{3 x})

e^{y} y^{^{'}} = x^{2}

\int 576 - 16 x^{2} d x

(2 y^{2} + 2 y + 4 x^{2}) d x + (2 x y + x) d y = 0

What is (\partial)/(\partial x)(3x^{3y}) ?
The answer to (\partial)/(\partial x)(3x^{3y}) is 9yx^{3y-1}