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Popular Calculus >

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

Solution

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

Solution

3 x^{2} - 2 x - 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of (e^{2x})/((1+e^{2x))^2}

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

t a y l or \frac{1}{x}

integral of (4sqrt(x)-1/(2sqrt(x)))

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

integral of 1/(y^2-16)

\int \frac{1}{y ^{2} - 16} d y

y^{^{'}} = t^{\frac{1}{4}} - y

Frequently Asked Questions (FAQ)

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