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Find the derivative of f(x) f(x) . Where f(x)=e(x+1) f(x)=e^{(x+1)} f′(x)=? f'(x) = ?

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Full solution

Q. Find the derivative of f(x) f(x) . Where f(x)=e(x+1) f(x)=e^{(x+1)} f′(x)=? f'(x) = ?
  1. Identify function: Identify the function to differentiate. f(x)=e(x+1)f(x) = e^{(x+1)}.
  2. Apply derivative rule: Apply the derivative rule for exponential functions. The derivative of eue^u, where uu is a function of xx, is eue^u times the derivative of uu.
  3. Find inner function derivative: Find the derivative of the inner function u(x)=x+1u(x) = x+1. The derivative of u(x)u(x) is 11.
  4. Multiply derivative and function: Multiply the derivative of the inner function by the original function. f′(x)=e(x+1)×1f'(x) = e^{(x+1)} \times 1.
  5. Simplify expression: Simplify the derivative expression. f′(x)=e(x+1)f'(x) = e^{(x+1)}.

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