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

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

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(\partial)/(\partial x)(x+xy^2)

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

1 + y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 1 + y^{2}

\int \frac{1}{sin ( x )} \frac{cos ( x )}{sin ( x )} d x

h \to 0 lim (\frac{( 1 + h ) 3 - 1}{h})

x, y \to (0, 0) lim (\frac{( 2 x ^{2} y )}{x ^{2} + y ^{4}})

x \to 2 + lim (3 - x)

\frac{d}{d x} (\frac{2 ^{x}}{cos ( x )})

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