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

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

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(\partial)/(\partial x)(x^2e^y+x-2y)

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

2 e^{y} x + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (2 y) = 0

= 2 e^{y} x + 1 - 0

Simplify

= 2 e^{y} x + 1

\int \frac{x ^{2} + 2 x + 1}{x ^{3} + x} d x

\frac{d y}{d x} = e^{y - x^{2} + 1}

\int 169 - t^{2} d t

x \frac{d y}{d x} + y = 6 x + 1

\int \frac{1}{( x - 4 ) ^{7}} d x

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