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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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

\frac{\partial}{\partial y} (x e^{y^{2}})

(y e^{x y} cos (2 x) - 2 e^{x y} sin (2 x) + 2 x) + (x e^{x y} cos (2 x) - 3) y^{^{'}} = 0

x \to 0 lim ((1 - 6 x)^{\frac{5}{x}})

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