Let h(x) = (2x + 1)⁵. Find h′(1). Give the answer as an integer.

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A power of a linear term

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Let $h (x) = (2 x + 1)^{5}$ . Find $h^{'} (1)$ . Give the answer as an integer.

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Hint

Treat the bracket as the inner function and remember to multiply by its derivative.

Solution

By the chain rule, $h^{'} (x) = 5 (2 x + 1)^{4} \times 2 = 10 (2 x + 1)^{4}$ .
At $x = 1$ the bracket equals $2 + 1 = 3$ , and $3 \times 3 \times 3 \times 3 = 81$ .
So $h^{'} (1) = 10 \times 81 = 810$ .

Answer: $810$