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

The answer to (\partial)/(\partial x)(4x^3y+xy^2) is 12yx^2+y^2

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

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

12 y x^{2} + y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4 x^{3} y) = 12 y x^{2}

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

= 12 y x^{2} + y^{2}

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

x^{3} - 6 x^{2} - 34 x + 40, at x = 4

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = - 4

\frac{\partial}{\partial z} (\frac{x y}{x + y + z})

\frac{d}{d x} (\frac{cos ( x )}{4 x})

What is (\partial)/(\partial x)(4x^3y+xy^2) ?
The answer to (\partial)/(\partial x)(4x^3y+xy^2) is 12yx^2+y^2