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

The derivative of sqrt(((x^2+1))/2) is x/(sqrt(2)\sqrt{x^2+1)}

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

The first derivative of sqrt(((x^2+1))/2) is x/(sqrt(2)\sqrt{x^2+1)}

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = \frac{sin ^{3} ( x ) + 4}{3 cos ^{3} ( x )}

2 x^{3} - 2.5 x - 5

y = \frac{1}{( sin ( x ) + cos ( x ) )}

cos (6 - 2 x)

t^{2} + 4 t + 5

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