What is (\partial)/(\partial x)(1+xy^2) ?

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

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(\partial)/(\partial x)(1+xy^2)

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

y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + y^{2}

Simplify

= y^{2}

h \to 0 lim (\frac{3}{h})

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\frac{d y}{d x} = - \frac{1}{2} y

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

\int 5 x^{2} + (\frac{2}{x})^{4} d x

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