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

compute the following derivatives using the formulas below.\n\n$m = \\frac{d}{dx}(6^{x})|_{x = 0} \\approx 1.792$\n\n$\\frac{d}{dx}6^{x} = m6^{x}$\n\n(a) $\\frac{d}{dx}(6^{x})|_{x = 5}$ (b) $\\frac{d}{dx}(6^{x})|_{x = -3}$\n\n(a) $\\frac{d}{dx}(6^{x})|_{x = 5} \\approx 13934.59$\n(round to two decimal places as needed.)\n\n(b) $\\frac{d}{dx}(6^{x})|_{x = -3} \\approx \\square$\n(round to two decimal places as needed.)

compute the following derivatives using the formulas below.\n\n$m = \\frac{d}{dx}(6^{x})|_{x = 0} \\approx 1.792$\n\n$\\frac{d}{dx}6^{x} = m6^{x}$\n\n(a) $\\frac{d}{dx}(6^{x})|_{x = 5}$ (b) $\\frac{d}{dx}(6^{x})|_{x = -3}$\n\n(a) $\\frac{d}{dx}(6^{x})|_{x = 5} \\approx 13934.59$\n(round to two decimal places as needed.)\n\n(b) $\\frac{d}{dx}(6^{x})|_{x = -3} \\approx \\square$\n(round to two decimal places as needed.)

Answer

Explanation:

Step1: Substitute into the formula

Given (\frac{d}{dx}6^{x}=m6^{x}) and (m = 1.792). For part (b), when (x=-3), we substitute (x=-3) into the formula (\frac{d}{dx}(6^{x})\big|_{x = - 3}=m\times6^{-3}).

Step2: Calculate the value

Since (6^{-3}=\frac{1}{6^{3}}=\frac{1}{216}), then (m\times6^{-3}=1.792\times\frac{1}{216}). [1.792\times\frac{1}{216}=\frac{1.792}{216}\approx0.01]

Answer:

(0.01)