What is the derivative of ln((x+sqrt(x^2+4)/2)) ?

The derivative of ln((x+sqrt(x^2+4)/2)) is 1/(sqrt(x^2+4))

What is the first derivative of ln((x+sqrt(x^2+4)/2)) ?

The first derivative of ln((x+sqrt(x^2+4)/2)) is 1/(sqrt(x^2+4))

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\frac{d}{d x} (ln (\frac{x + x ^{2} + 4}{2}))

\frac{1}{x ^{2} + 4}

Solution steps

\frac{d}{d x} (ln (\frac{x + x ^{2} + 4}{2}))

Apply the chain rule:

\frac{1}{\frac{x + x ^{2} + 4}{2}} \frac{d}{d x} (\frac{x + x ^{2} + 4}{2})

= \frac{1}{\frac{x + x ^{2} + 4}{2}} \frac{d}{d x} (\frac{x + x ^{2} + 4}{2})

\frac{d}{d x} (\frac{x + x ^{2} + 4}{2}) = \frac{1}{2} (1 + \frac{x}{x ^{2} + 4})

= \frac{1}{\frac{x + x ^{2} + 4}{2}} \cdot \frac{1}{2} (1 + \frac{x}{x ^{2} + 4})

Simplify

\frac{1}{\frac{x + x ^{2} + 4}{2}} \cdot \frac{1}{2} (1 + \frac{x}{x ^{2} + 4}) : \frac{1}{x ^{2} + 4}

= \frac{1}{x ^{2} + 4}

f (x) = e^{x} - x - 2

\frac{\partial}{\partial x} (e^{x} + 3 e^{y})

\frac{d y}{d x}, x y = x^{5} y + 34

\frac{d}{d x} (\frac{3}{sin ( x )})

y^{^{'}} = e^{(5 x + 4 y)}

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