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

The answer to (\partial)/(\partial x)((x^2+2)(x^3+1)) is 5x^4+6x^2+2x

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

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

5 x^{4} + 6 x^{2} + 2 x

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} + 2, g = x^{3} + 1

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

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

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

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

Simplify

2 x (x^{3} + 1) + 3 x^{2} (x^{2} + 2) : 5 x^{4} + 6 x^{2} + 2 x

= 5 x^{4} + 6 x^{2} + 2 x

x \to - 5 + lim (\frac{- 1}{x ^{2} - 25})

\frac{d}{d x} (g (x) \cdot (a x^{2} + x))

n = 2 \sum \infty \frac{( 3 ^{3 n} )}{2 ^{2 n - 2}}

x \to 10 lim (\frac{x}{x ^{2} - 100})

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

What is (\partial)/(\partial x)((x^2+2)(x^3+1)) ?
The answer to (\partial)/(\partial x)((x^2+2)(x^3+1)) is 5x^4+6x^2+2x