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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = x + 1

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

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

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

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

Simplify

\frac{1}{2 x} (x + 1) + \frac{1}{2 x} x : \frac{x + 1}{2 x} + \frac{1}{2}

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

Popular Examples

derivative of 4x^3-2/(x^3)

\frac{d}{d x} (4 x^{3} - \frac{2}{x ^{3}})

y^{^{''}} - y^{^{'}} = - 12

integral of 4/((t^2+1)^{3/2)}

\int \frac{4}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

integral from 0 to 1 of pi(x-x^8)

\int_{0}^{1} π (x - x^{8}) d x

integral from 1 to infinity of x^{-4}

\int_{1}^{\infty} x^{- 4} d x

Frequently Asked Questions (FAQ)

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