Derivative of 1/x

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

\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?

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

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.