What is (\partial)/(\partial x)(y^8+4x^3y^3) ?

The answer to (\partial)/(\partial x)(y^8+4x^3y^3) is 12y^3x^2

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(\partial)/(\partial x)(y^8+4x^3y^3)

\frac{\partial}{\partial x} (y^{8} + 4 x^{3} y^{3})

12 y^{3} x^{2}

Solution steps

\frac{\partial}{\partial x} (y^{8} + 4 x^{3} y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y^{8}) + \frac{\partial}{\partial x} (4 x^{3} y^{3})

\frac{\partial}{\partial x} (y^{8}) = 0

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

= 0 + 12 y^{3} x^{2}

Simplify

= 12 y^{3} x^{2}

[x^{2} (x^{2} + 6 x)]^{6}

\int \frac{( x ^{2} - x + 12 )}{x ^{3} + 3 x} d x

4 v^{2} - 2

x \to 0 lim (\frac{1}{x} sin (\frac{1}{x}))

\int 18 cos^{2} (x) sin (x) d x

What is (\partial)/(\partial x)(y^8+4x^3y^3) ?
The answer to (\partial)/(\partial x)(y^8+4x^3y^3) is 12y^3x^2