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Popular >

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

Solution

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

Solution

4 x^{3} + 3 x^{2} + 2 x - 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (x^{3} + x - 2) + (3 x^{2} + 1) (x + 1) : 4 x^{3} + 3 x^{2} + 2 x - 1

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

Popular Examples

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\int \frac{5}{( x - 1 ) ( x ^{2} + 4 )} d x

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8x^7y+x^8y^'=-5sec^2(x)tan(x)

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derivative of-x+y+2

\frac{d}{d x} (- x + y + 2)

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x \to \frac{π}{6} lim (\frac{sin ( x ) - sin ( \frac{π}{6} )}{x - \frac{π}{6}})

Frequently Asked Questions (FAQ)

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