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

The derivative of x-sqrt(2+((x+1)^2)/2) is 1-(x+1)/(sqrt(2)\sqrt{x^2+2x+5)}

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

The first derivative of x-sqrt(2+((x+1)^2)/2) is 1-(x+1)/(sqrt(2)\sqrt{x^2+2x+5)}

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derivative of

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

1 - \frac{x + 1}{2 x ^{2} + 2 x + 5}

Solution steps

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

Simplify

x - 2 + \frac{( x + 1 ) ^{2}}{2} : x - \frac{x ^{2} + 2 x + 5}{2}

= \frac{d}{d x} (x - \frac{x ^{2} + 2 x + 5}{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} - \frac{d}{d x} (\frac{x ^{2} + 2 x + 5}{2})

\frac{d x}{d x} = 1

\frac{d}{d x} (\frac{x ^{2} + 2 x + 5}{2}) = \frac{x + 1}{2 x ^{2} + 2 x + 5}

= 1 - \frac{x + 1}{2 x ^{2} + 2 x + 5}

\int_{0}^{1} π (y - y^{2}) d y

\frac{\partial}{\partial x} (x e^{z})

\int e^{i t} d t

x \to \infty lim (\frac{7}{x} - 1)

What is the derivative of x-sqrt(2+((x+1)^2)/2) ?
The derivative of x-sqrt(2+((x+1)^2)/2) is 1-(x+1)/(sqrt(2)\sqrt{x^2+2x+5)}
What is the first derivative of x-sqrt(2+((x+1)^2)/2) ?
The first derivative of x-sqrt(2+((x+1)^2)/2) is 1-(x+1)/(sqrt(2)\sqrt{x^2+2x+5)}