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Popular Calculus >

derivative of (x^2+1(x^3+1))

Solution

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

Solution

5 x^{4} + 3 x^{2} + 2 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 5 x^{4} + 3 x^{2} + 2 x

Graph

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in v erse l a pl a ce \frac{( \frac{1}{2} )}{s}

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\int 3 x^{\frac{1}{8}} d x

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\frac{\partial}{\partial x} (e^{2})

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s l o p e - 3 x^{2} + 3 x + 1, at x = 1

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+1(x^3+1)) ?
The derivative of (x^2+1(x^3+1)) is 5x^4+3x^2+2x
What is the first derivative of (x^2+1(x^3+1)) ?
The first derivative of (x^2+1(x^3+1)) is 5x^4+3x^2+2x