What is (\partial)/(\partial x)(x^3y^2+2x^2y+x-1) ?

The answer to (\partial)/(\partial x)(x^3y^2+2x^2y+x-1) is 3x^2y^2+4xy+1

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(\partial)/(\partial x)(x^3y^2+2x^2y+x-1)

\frac{\partial}{\partial x} (x^{3} y^{2} + 2 x^{2} y + x - 1)

3 x^{2} y^{2} + 4 x y + 1

Solution steps

\frac{\partial}{\partial x} (x^{3} y^{2} + 2 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^{3} y^{2}) + \frac{\partial}{\partial x} (2 x^{2} y) + \frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (2 x^{2} y) = 4 y x

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

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

= 3 y^{2} x^{2} + 4 y x + 1 - 0

Simplify

= 3 x^{2} y^{2} + 4 x y + 1

\int 3 sec^{- 2} (x t a) n^{3} x d x

x \to 9 lim (2 x^{2} - 3)

v (t) = 30 - t^{2}

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

t^{2} cos (4 t)

What is (\partial)/(\partial x)(x^3y^2+2x^2y+x-1) ?
The answer to (\partial)/(\partial x)(x^3y^2+2x^2y+x-1) is 3x^2y^2+4xy+1