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Popular >

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

Solution

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

Solution

3 x^{2} - 6 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (x - 2)^{2} + 2 (x - 2) (x + 1) : 3 x^{2} - 6 x

= 3 x^{2} - 6 x

Graph

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sum from n=1 to infinity of 3/(n^2+5n+4)

n = 1 \sum \infty \frac{3}{n ^{2} + 5 n + 4}

limit as x approaches-4+of (x+5)/(x+4)

x \to - 4 + lim (\frac{x + 5}{x + 4})

area 2x^3-x^2-5x,-x^2+3x,0,2 area

2 x^{3} - x^{2} - 5 x, - x^{2} + 3 x, 0, 2

(dy)/(dx)= 1/(sqrt(4-x^2)),y(0)=pi

\frac{d y}{d x} = \frac{1}{4 - x ^{2}}, y (0) = π

integral of 5tan^3(x)sec(x)

\int 5 tan^{3} (x) sec (x) d x

Frequently Asked Questions (FAQ)

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