What is (\partial)/(\partial x)(3xy-x^2y^2+23) ?

The answer to (\partial)/(\partial x)(3xy-x^2y^2+23) is -2xy^2+3y

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(\partial)/(\partial x)(3xy-x^2y^2+23)

\frac{\partial}{\partial x} (3 x y - x^{2} y^{2} + 23)

- 2 x y^{2} + 3 y

Solution steps

\frac{\partial}{\partial x} (3 x y - x^{2} y^{2} + 23)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x y) - \frac{\partial}{\partial x} (x^{2} y^{2}) + \frac{\partial}{\partial x} (23)

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

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

\frac{\partial}{\partial x} (23) = 0

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

Simplify

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

\frac{d y}{d x} = \frac{x}{e ^{y}}

3 x^{2} - 2

f (x) = - 9.8 x^{2} + 2 x + 1

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

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

What is (\partial)/(\partial x)(3xy-x^2y^2+23) ?
The answer to (\partial)/(\partial x)(3xy-x^2y^2+23) is -2xy^2+3y