Evaluate second derivative of sin(x): animated lesson

1. 1. The problem
   Finding a derivative

   $\frac{d^{2}}{dx^{2}}\left[\sin\left( x\right)\right]$
2. 2. Steps, part 1
   1. $$\frac{d}{dx}\left[\sin\left( x\right)\right]$$
      Derivative number 1
   2. $$\frac{d}{dx}\left[\sin\left( x\right)\right] = \cos\left( x\right)$$
      d/dx[sin x] = cos x
   3. $$f'(x) = \cos\left( x\right)$$
      Simplify the first derivative
   4. $$\frac{d}{dx}\left[\cos\left( x\right)\right]$$
      Derivative number 2
3. 3. Steps, part 2
   1. $$\frac{d}{dx}\left[\cos\left( x\right)\right] = -\sin\left( x\right)$$
      d/dx[cos x] = −sin x
   2. $$f''(x) = -\sin\left( x\right)$$
      Simplify the second derivative
4. 4. The answer
   $$f''(x) = -\sin\left( x\right)$$

   f''(x) = -sin(x)

5. 5. 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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