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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

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\int \frac{4 x + 1}{2 x ^{2} + x - 3} d x

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in v erse l a pl a ce \frac{4}{s ( s ^{2} + 4 )}

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

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

tangent of f(x)= x/(x^2+9),\at x=0

t an g e n t f (x) = \frac{x}{x ^{2} + 9}, at x = 0

derivative of y=sqrt(3x^2-4)

d er i v a t i v e y = 3 x^{2} - 4

Frequently Asked Questions (FAQ)

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