Derivative of 1/x

\frac{d}{dx}\left[\frac{1}{x}\right] = -\frac{1}{x^{2}}.

Differentiate again: \frac{d^2}{dx^2}\left[\frac{1}{x}\right] = \frac{2}{x^{3}}.

Plug into the derivative: f'(3.1) = -0.104058. That is the slope of the tangent line there; drag the graph to see it.

\frac{d}{dx}\left[\frac{1}{x}\right] = -\frac{1}{x^{2}}

Rewrite as x⁻¹. The derivative −1/x² is negative everywhere, since the hyperbola is always falling on each side of x = 0.

Power rule
d/dx[xⁿ] = n·xⁿ⁻¹.
$\frac{d}{dx}\left[\frac{1}{x}\right] = -\frac{1}{x^{2}}$

Drag the graph · at x = 3.32 the slope is -0.090724, the height of the dashed curve.

Questions students ask

What is the derivative of 1/x?

$\frac{d}{dx}\left[\frac{1}{x}\right] = -\frac{1}{x^{2}}$ .

What is the second derivative of 1/x?

Differentiate again: $\frac{d^2}{dx^2}\left[\frac{1}{x}\right] = \frac{2}{x^{3}}$ .

What is the slope of 1/x at x = 3.1?

Plug into the derivative: $f'(3.1) = -0.104058$ . That is the slope of the tangent line there; drag the graph to see it.

How do you find the derivative of 1/x?

Rewrite as x⁻¹. The derivative −1/x² is negative everywhere, since the hyperbola is always falling on each side of x = 0.

What is the integral of 1/x?

See the integral of 1/x page for the antiderivative with steps.