Find the derivative of e^(sin x): animated lesson

1. 1. The problem
   Finding a derivative

   $\frac{d}{dx}\left[{e}^{\sin\left( x\right)}\right]$
2. 2. Step by step
   1. $$\frac{d}{dx}\left[{e}^{\sin\left( x\right)}\right] = {e}^{\sin\left( x\right)} \cos\left( x\right)$$
      Exponential rule: d/dx[eᵘ] = eᵘ·u′
   2. $$\frac{d}{dx}\left[\sin\left( x\right)\right] = \cos\left( x\right)$$
      d/dx[sin x] = cos x
   3. $$f'(x) = {e}^{\sin\left( x\right)} \cos\left( x\right)$$
      Combine and simplify
3. 3. The answer
   $$f'(x) = {e}^{\sin\left( x\right)} \cos\left( x\right)$$

   f'(x) = e^sin(x)·cos(x)

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

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