Solve any maths problem

Step by step

1. \frac{d}{dx}\left[\log{\left(x^{2} + 1 \right)}\right]

   Start from the derivative to compute.

2. \frac{\frac{d}{d x} \left(x^{2} + 1\right)}{x^{2} + 1}

   Chain rule: (ln u)′ = 1/u, times u′ where u = x^{2} + 1.

3. \frac{\frac{d}{d x} 1 + \frac{d}{d x} x^{2}}{x^{2} + 1}

   Sum rule: differentiate term by term.

4. \frac{\frac{d}{d x} x^{2}}{x^{2} + 1}

   The derivative of a constant is 0.

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

   Power rule: (xⁿ)′ = n·xⁿ⁻¹ with n = 2.

Reveal the answer

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