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

The answer to (\partial)/(\partial x)(x+y+x^3y^2) is 3x^2y^2+1

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

= 1 + 0 + 3 y^{2} x^{2}

Simplify

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

\int \frac{1}{x ( x ^{2} + x + 1 )} d x

\int 9 x^{5} e^{x} d x

\frac{1}{s ( s ^{2} + 200 )}

x^{e^{x}}

\frac{d}{d x} (2 x^{3} - 21 x^{2} + 60 x)

What is (\partial)/(\partial x)(x+y+x^3y^2) ?
The answer to (\partial)/(\partial x)(x+y+x^3y^2) is 3x^2y^2+1