a. find the derivative function f’ for the function f. b. determine an equation of the line tangent to the…
a. find the derivative function f’ for the function f. b. determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. f(x)=2/(3x + 1),a = - 1 a. f’(x)=
Answer
Answer:
$-\frac{6}{(3x + 1)^2}$
Explanation:
Step1: Apply quotient - rule
The quotient - rule states that if $y=\frac{u}{v}$, then $y^\prime=\frac{u^\prime v - uv^\prime}{v^2}$. Here, $u = 2$, $u^\prime=0$, $v = 3x + 1$, and $v^\prime=3$.
Step2: Substitute values
$f^\prime(x)=\frac{0\times(3x + 1)-2\times3}{(3x + 1)^2}$.
Step3: Simplify
$f^\prime(x)=\frac{- 6}{(3x + 1)^2}$.