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Popular >

derivative of sqrt(x+1)(x-1)

Solution

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

Solution

\frac{3 x + 1}{2 x + 1}

Solution steps

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

Apply the Product Rule:

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

f = x + 1, g = x - 1

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

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

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

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

Simplify

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

= \frac{3 x + 1}{2 x + 1}

Popular Examples

limit as x approaches 0 of 1/(x^{13)}

x \to 0 lim (\frac{1}{x ^{13}})

(x^2+1)(dy)/(dx)=x^2(y-1)

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

derivative of xysqrt(1-(x^2/4-(y^2)/9))

\frac{d}{d x} (x y 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9})

derivative of f(x)=(x^3+2x^2+x-1)/x derivative of

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

sum from n=0 to infinity of (-1)^n(2)^n

n = 0 \sum \infty (- 1)^{n} (2)^{n}

Frequently Asked Questions (FAQ)

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