Use the chain rule to find the derivative of each of the following : a. [tex]\frac{2}{(3x^2-x+7)^3}[/tex] b. [tex](4x-10)^ July 31, 2021 by Huyền Thanh Use the chain rule to find the derivative of each of the following : a. \frac{2}{(3x^2-x+7)^3} b. (4x-10)^1^0
Answer: see explanation Step-by-step explanation: Using the chain rule Given y = f(g(x)), then [tex]\frac{dy}{dx}[/tex] = f'(g(x)) × g'(x) (a) y = [tex]\frac{2}{(3x^2-x+7)^3}[/tex] = 2 ([tex]3x^2-x+7)^{-3}[/tex] [tex]\frac{dy}{dx}[/tex] = 2. – 3 [tex](3x^2-x+7)^{-4}[/tex] × [tex]\frac{d}{dx}[/tex] (3x² – x + 7) = – 6 [tex](3x^2-x+7)^{-4}[/tex] × (6x – 1) = [tex]\frac{-6(6x-1)}{(3x^2-x+7)^4}[/tex] ————————————————— (b) y = [tex](4x-10)^{10}[/tex] [tex]\frac{dy}{dx}[/tex] = 10[tex](4x-10)^{9}[/tex] × [tex]\frac{d}{dx}[/tex](4x – 10) = 10[tex](4x-10)^{9}[/tex] × 4 = 40[tex](4x-10)^{9}[/tex] Reply
Answer:
see explanation
Step-by-step explanation:
Using the chain rule
Given
y = f(g(x)), then
[tex]\frac{dy}{dx}[/tex] = f'(g(x)) × g'(x)
(a)
y = [tex]\frac{2}{(3x^2-x+7)^3}[/tex] = 2 ([tex]3x^2-x+7)^{-3}[/tex]
[tex]\frac{dy}{dx}[/tex] = 2. – 3 [tex](3x^2-x+7)^{-4}[/tex] × [tex]\frac{d}{dx}[/tex] (3x² – x + 7)
= – 6 [tex](3x^2-x+7)^{-4}[/tex] × (6x – 1)
= [tex]\frac{-6(6x-1)}{(3x^2-x+7)^4}[/tex]
—————————————————
(b)
y = [tex](4x-10)^{10}[/tex]
[tex]\frac{dy}{dx}[/tex] = 10[tex](4x-10)^{9}[/tex] × [tex]\frac{d}{dx}[/tex](4x – 10)
= 10[tex](4x-10)^{9}[/tex] × 4
= 40[tex](4x-10)^{9}[/tex]