Differentiate tan(3x): animated lesson

1. 1. The problem
   Finding a derivative

   $\frac{d}{dx}\left[\tan\left(3x\right)\right]$
2. 2. Step by step
   1. $$\frac{d}{dx}\left[\tan\left(3x\right)\right] = 3 {\sec\left(3x\right)}^{2}$$
      Chain rule — d/dx[tan u] = sec² u · u′
   2. $$\frac{d}{dx}\left[3x\right] = 3$$
      Constant multiple rule
   3. $$f'(x) = 3 {\sec\left(3x\right)}^{2}$$
      Combine and simplify
3. 3. The answer
   $$f'(x) = 3 {\sec\left(3x\right)}^{2}$$

   f'(x) = 3sec(3x)²

4. 4. Check
   • ✓Cross-checked numerically against an independent symbolic differentiator at 8 sample points ✓

Differentiate with the power, product, quotient and chain rules, including higher derivatives.

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