What is (\partial)/(\partial x)(x^2y+x+1) ?

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

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(\partial)/(\partial x)(x^2y+x+1)

\frac{\partial}{\partial x} (x^{2} y + x + 1)

2 x y + 1

Solution steps

\frac{\partial}{\partial x} (x^{2} y + x + 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (1)

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

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

\frac{\partial}{\partial x} (1) = 0

= 2 y x + 1 + 0

Simplify

= 2 x y + 1

e^{5 x}

\int (x^{3} e^{- x^{2}}) d x

\int sin (ln (3 x)) d x

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

\int_{0}^{l n (2)} e^{2 x} d x

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