CalcRef

Derivatives · Inverse Trigonometric

Derivative of arccot(x)

ddx[arccot x]=−11+x2\frac{d}{dx}[\text{arccot}\, x] = -\frac{1}{1 + x^2}

The derivative of the inverse cotangent function. Note the negative sign compared to arctan.

Worked examples

Find d/dx[arccot(5x)].
  1. Chain rule: -1/(1+(5x)²) · 5 = -5/(1+25x²)

Answer: -5/(1 + 25x²)

Verify that d/dx[arctan x + arccot x] = 0.
  1. 1/(1+x²) + (-1/(1+x²)) = 0 ✓

Answer: 0

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