What is (\partial)/(\partial x)(yx^2+6x^3+xy) ?

The answer to (\partial)/(\partial x)(yx^2+6x^3+xy) is 2yx+18x^2+y

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(\partial)/(\partial x)(yx^2+6x^3+xy)

\frac{\partial}{\partial x} (y x^{2} + 6 x^{3} + x y)

2 y x + 18 x^{2} + y

Solution steps

\frac{\partial}{\partial x} (y x^{2} + 6 x^{3} + x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y x^{2}) + \frac{\partial}{\partial x} (6 x^{3}) + \frac{\partial}{\partial x} (x y)

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

\frac{\partial}{\partial x} (6 x^{3}) = 18 x^{2}

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

= 2 y x + 18 x^{2} + y

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

\frac{d}{d x} (3 x^{2} + 5 x + 8)

\int cos (6 t) d t

4 2 x, 2 x^{2}, - 4 x + 6

(t + 2) y^{'} + y = \frac{1}{t - 1}

What is (\partial)/(\partial x)(yx^2+6x^3+xy) ?
The answer to (\partial)/(\partial x)(yx^2+6x^3+xy) is 2yx+18x^2+y