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

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

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

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

4 x^{3} + 2 y x

Solution steps

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

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} (x^{2} y)

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

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

= 4 x^{3} + 2 y x

\int \frac{441 - x ^{2}}{x} d x

y = - x^{3} + 2 x^{2} + 1

\int \frac{e ^{3 x}}{1 + e ^{6 x}} d x

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

\frac{d}{d x} (e^{6 x} ln (x^{2} - 4))

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