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Popular >

derivative of (x^4-1(x^2+1))

Solution

\frac{d}{d x} ((x^{4} - 1) (x^{2} + 1))

Solution

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

Solution steps

\frac{d}{d x} ((x^{4} - 1) (x^{2} + 1))

Apply the Product Rule:

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

f = x^{4} - 1, g = x^{2} + 1

= \frac{d}{d x} (x^{4} - 1) (x^{2} + 1) + \frac{d}{d x} (x^{2} + 1) (x^{4} - 1)

\frac{d}{d x} (x^{4} - 1) = 4 x^{3}

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

= 4 x^{3} (x^{2} + 1) + 2 x (x^{4} - 1)

Simplify

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

= 6 x^{5} + 4 x^{3} - 2 x

Popular Examples

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\int (8 x^{5} - 8 x^{- 3}) d x

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\frac{10}{s ( s ^{2} + 10 s + 50 )}

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x \to - 4 lim (6 x + 1)

integral of (2x^2+x-1)/(x^3-2x^2+x)

\int \frac{2 x ^{2} + x - 1}{x ^{3} - 2 x ^{2} + x} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^4-1(x^2+1)) ?
The derivative of (x^4-1(x^2+1)) is 6x^5+4x^3-2x
What is the first derivative of (x^4-1(x^2+1)) ?
The first derivative of (x^4-1(x^2+1)) is 6x^5+4x^3-2x