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

The answer to (\partial)/(\partial x)(x^4-yx^2+2y^3) is 4x^3-2xy

Popular >

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

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

4 x^{3} - 2 x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (2 y^{3}) = 0

= 4 x^{3} - 2 y x + 0

Simplify

= 4 x^{3} - 2 x y

\frac{d y}{d x} = 3 y + 4

\int cos^{4} (7 x + 2) d x

y = 6 e^{x} + x, (0, 6)

\frac{\partial}{\partial x} (e^{z} + \frac{1}{x} + x e^{- y})

\int 2^{5} d x

What is (\partial)/(\partial x)(x^4-yx^2+2y^3) ?
The answer to (\partial)/(\partial x)(x^4-yx^2+2y^3) is 4x^3-2xy