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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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

\frac{d}{d x} (\frac{- 200 ln ( \frac{x}{40} )}{x + 20})

\int_{0}^{15} 2 π x (15 x - x^{2}) d x

\frac{\partial}{\partial x} (ln (\frac{2 x y}{5 z}))

\int - \frac{9}{x ^{10}} d x

\frac{\partial}{\partial x} (u)

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