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Popular >

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

Solution

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

Solution

18 x^{2} + 22 x + 6

Solution steps

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

Apply the Product Rule:

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

f = x + 1, g = (2 x + 1) (3 x + 1)

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

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

\frac{d}{d x} ((2 x + 1) (3 x + 1)) = 12 x + 5

= 1 \cdot (2 x + 1) (3 x + 1) + (12 x + 5) (x + 1)

Simplify

1 \cdot (2 x + 1) (3 x + 1) + (12 x + 5) (x + 1) : 18 x^{2} + 22 x + 6

= 18 x^{2} + 22 x + 6

Popular Examples

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x \to 0 lim (- 3)

d/(dt)(e^{t/7}sin(t/7))

\frac{d}{d t} (e^{\frac{t}{7}} sin (\frac{t}{7}))

(\partial)/(\partial x)(y+2/(x^2))

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

tangent of 7x^2+xy+7y^2=15,(1,1)tangent of

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x \to 0 + lim ((e^{x} + x)^{\frac{1}{x}})

Frequently Asked Questions (FAQ)

What is the derivative of (x+1(2x+1)(3x+1)) ?
The derivative of (x+1(2x+1)(3x+1)) is 18x^2+22x+6
What is the first derivative of (x+1(2x+1)(3x+1)) ?
The first derivative of (x+1(2x+1)(3x+1)) is 18x^2+22x+6