compute the following derivatives using the formulas below.\nm = \\frac{d}{dx}(6^{x})|_{x = 0} \\approx…

compute the following derivatives using the formulas below.\nm = \\frac{d}{dx}(6^{x})|_{x = 0} \\approx 1.792\n\\frac{d}{dx}6^{x}=m6^{x}\n(a) \\frac{d}{dx}(6^{x})|_{x = 5}\n(b) \\frac{d}{dx}(6^{x})|_{x = -3}\n(a) \\frac{d}{dx}(6^{x})|_{x = 5} \\approx \\square\n(round to two decimal places as needed.)

compute the following derivatives using the formulas below.\nm = \\frac{d}{dx}(6^{x})|_{x = 0} \\approx 1.792\n\\frac{d}{dx}6^{x}=m6^{x}\n(a) \\frac{d}{dx}(6^{x})|_{x = 5}\n(b) \\frac{d}{dx}(6^{x})|_{x = -3}\n(a) \\frac{d}{dx}(6^{x})|_{x = 5} \\approx \\square\n(round to two decimal places as needed.)

Answer

Explanation:

Step1: Substitute into the derivative formula

Given (\frac{d}{dx}6^{x}=m6^{x}) with (m = 1.792). For part (a), when (x = 5), we substitute (x) into the formula (\frac{d}{dx}(6^{x})\big|_{x = 5}=m\times6^{5}).

Step2: Calculate the value

We know that (6^{5}=6\times6\times6\times6\times6 = 7776). Then (m\times6^{5}=1.792\times7776). [1.792\times7776=(1 + 0.792)\times7776=7776+0.792\times7776] [0.792\times7776=(0.8 - 0.008)\times7776=0.8\times7776-0.008\times7776] [0.8\times7776 = 6220.8], [0.008\times7776=62.208] [0.792\times7776=6220.8- 62.208=6158.592] [7776+6158.592=13934.592\approx13934.59]

Answer:

(13934.59)