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

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

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

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

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

Solution steps

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

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

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

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

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

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

Simplify

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

\int \frac{1}{X ^{2}} D X d X

n = 0 \sum \infty 20000

g (x) = \frac{9 ln ( x )}{4 x + 5}

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

y = 10 csc (9 x^{4} - 9 x + 4)

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