Respuesta :
Answer: a) -24
b) [tex]-\frac{36}{25}[/tex]
c) 4
Step-by-step explanation:
a) To determine the value of (fg)', use the product rule of derivative, i.e.:
(fg)'(x) = f'(x)g(x) + f(x)g'(x)
(fg)'(5) = f'(5)g(5) + f(5)g'(5)
(fg)'(5) = 6(-5) + 3(2)
(fg)'(5) = -24
b) The value is given by the use of the quotient rule of derivative:
[tex](\frac{f}{g})'(x)=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}[/tex]
[tex](\frac{f}{g})' (5)=\frac{f'(5)g(5)-f(5)g'(5)}{[g(5)]^2}[/tex]
[tex](\frac{f}{g})'(5)=\frac{6(-5)-3(2)}{(-5)^{2}}[/tex]
[tex](\frac{f}{g})'(5)=\frac{-36}{25}[/tex]
c) [tex](\frac{g}{f})'(5)=\frac{g'(5)f(5)-g(5)f'(5)}{[f(5)]^{2}}[/tex]
[tex](\frac{g}{f})'(5)=\frac{2(3)-(-5)(6)}{3^{2}}[/tex]
[tex](\frac{g}{f})'(5)=\frac{36}{9}[/tex]
[tex](\frac{g}{f})'(5)=4[/tex]
