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

The answer to (\partial)/(\partial x)((z)(y^2-3x^3y)) is -9zyx^2

Popular >

(\partial)/(\partial x)((z)(y^2-3x^3y))

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

- 9 zy x^{2}

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (3 x^{3} y) = 9 y x^{2}

= z (0 - 9 y x^{2})

Simplify

= - 9 zy x^{2}

\frac{( x ^{2} + x + 1 )}{( x + 1 ) ^{2} ( x + 2 )}

\frac{z ^{2}}{( z + 6 ) ( z + 9 )}

A (1, - 2) B (5, - 5)

\frac{2 ( - 1 ) ^{k} + 2 \cdot 3 ^{1 + k} + 3 ( - 1 ) ^{k - 1} + 1}{2}

\frac{( - 1 ) ^{n} n ( n - 1 ) x ^{n - 2}}{2 \cdot 5 ^{n + 1}}

What is (\partial)/(\partial x)((z)(y^2-3x^3y)) ?
The answer to (\partial)/(\partial x)((z)(y^2-3x^3y)) is -9zyx^2