What is (\partial)/(\partial y)((M)(y^3+kxy^4-2x)) ?

The answer to (\partial)/(\partial y)((M)(y^3+kxy^4-2x)) is M(4ky^3x+3y^2)

Popular >

(\partial)/(\partial y)((M)(y^3+kxy^4-2x))

\frac{\partial}{\partial y} ((M) (y^{3} + k x y^{4} - 2 x))

M (4 k y^{3} x + 3 y^{2})

Solution steps

\frac{\partial}{\partial y} ((M) (y^{3} + k x y^{4} - 2 x))

Treat

k, M, x

as constants

Take the constant out:

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

= M \frac{\partial}{\partial y} (y^{3} + k x y^{4} - 2 x)

Apply the Sum/Difference Rule:

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

= M (\frac{\partial}{\partial y} (y^{3}) + \frac{\partial}{\partial y} (k x y^{4}) - \frac{\partial}{\partial y} (2 x))

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

\frac{\partial}{\partial y} (k x y^{4}) = 4 x k y^{3}

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

= M (3 y^{2} + 4 x k y^{3} - 0)

Simplify

= M (4 k y^{3} x + 3 y^{2})

(-) (x + 1) (- x + 3)

\frac{p ( s - 2 )}{2}

\frac{5 ( 4 x ^{5} + 1 ) ( x + x ^{5} - 1 ) ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

\frac{( r + pB ) ( 1 + l s B )}{( 1 + r pB ) ( l + s B )}

\frac{( a + c ) ( a - c )}{4 b}

What is (\partial)/(\partial y)((M)(y^3+kxy^4-2x)) ?
The answer to (\partial)/(\partial y)((M)(y^3+kxy^4-2x)) is M(4ky^3x+3y^2)