What is (\partial)/(\partial y)(5x^3y^6) ?

The answer to (\partial)/(\partial y)(5x^3y^6) is 30x^3y^5

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(\partial)/(\partial y)(5x^3y^6)

\frac{\partial}{\partial y} (5 x^{3} y^{6})

30 x^{3} y^{5}

Solution steps

\frac{\partial}{\partial y} (5 x^{3} y^{6})

Treat

x

as a constant

Take the constant out:

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

= 5 x^{3} \frac{\partial}{\partial y} (y^{6})

Apply the Power Rule:

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

= 5 x^{3} \cdot 6 y^{6 - 1}

Simplify

= 30 x^{3} y^{5}

\frac{y ^{^{'}} + 0.3334 y}{( 20.004 x + 6000 )} = 20

2 x y + x^{3} = x \frac{d y}{d x}

f (x) = x^{3} - 3 (x)^{2} + 4 (x) + 5

(1 + x) cos (x), at x = 0

9 x - x^{2}, 2 x

What is (\partial)/(\partial y)(5x^3y^6) ?
The answer to (\partial)/(\partial y)(5x^3y^6) is 30x^3y^5