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Find the derivative of (2x + 1)^5

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Answer
10(2x+1)4\boxed{10(2x + 1)^4}

We can check this result by using the chain rule, where we bring down the exponent, reduce it by one, and multiply by the derivative of the inside function.

Problem: Find the derivative of f(x)=(2x+1)5f(x) = (2x + 1)^5.

Steps

  1. Apply the chain rule
    ddx[(2x+1)5]=5(2x+1)4⋅ddx(2x+1)\frac{d}{dx}[(2x + 1)^5] = 5(2x + 1)^{4} \cdot \frac{d}{dx}(2x + 1)
  2. Differentiate the inner function
    5(2x+1)4⋅25(2x + 1)^{4} \cdot 2
  3. Simplify the expression
    10(2x+1)410(2x + 1)^4

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