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Popular >

derivative of (sqrt(1+x)/2)

Solution

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

Solution

\frac{1}{4 1 + x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2} \cdot \frac{1}{2 1 + x} \cdot 1 : \frac{1}{4 1 + x}

= \frac{1}{4 1 + x}

Popular Examples

integral of 1/((x-9)sqrt(x^2-18x))

\int \frac{1}{( x - 9 ) x ^{2} - 18 x} d x

expand 2/((-x^3+9x)^4)expand

\frac{2}{( - x ^{3} + 9 x ) ^{4}}

integral of x/(1+x)

\int \frac{x}{1 + x} d x

y^'=1+x-y-xy,y(0)=-1

y^{^{'}} = 1 + x - y - x y, y (0) = - 1

limit as x approaches pi of-4sin(x/2)

x \to π lim (- 4 sin (\frac{x}{2}))

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(1+x)/2) ?
The derivative of (sqrt(1+x)/2) is 1/(4sqrt(1+x))
What is the first derivative of (sqrt(1+x)/2) ?
The first derivative of (sqrt(1+x)/2) is 1/(4sqrt(1+x))