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

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

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

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

2 x (1 + y)^{3}

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= (1 + y)^{3} \cdot 2 x^{2 - 1}

Simplify

= 2 x (1 + y)^{3}

\frac{s}{s + 1000}

\frac{d}{d y} (\frac{e ^{y} + e ^{- y}}{2})

y^{^{''}} - 2 y^{^{'}} + 3 y = 0

\frac{d}{d x} (\frac{1}{3} sin^{3} (x) - sin (x) + 1)

x \to 4 lim (\frac{x + 4}{x + 7})

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