Question

Hallar la derivada de:

1) f(x) = (5x²+3x) / (2x+8)

2) g(x) = L(x) + 2/(x+1)

3) h(x) = (5x+3) / (x.e^x)

(L = logaritmo neperiano [en base e])

Answer 1

f(x)=y=(5x²+3x) / (2x+8)

dy=((10x+3)(2x+8)-(5x²+3x)(2))/(2x+8)^2

resolviendo

dy=10x^2+80x+24/(2x+8)^2

 

2) g(x) = L(x) + (2/x+1)

g'(x) =L'(x)+ 2(x^-1)+0

g'(x)=L'(x)-2/x^2

 

3) h(x) = (5x+3) / (x.e^x) 

dy=5(x.e^x)-(5x+3)(e^x+ x.e^x) / (x.e^x)^2

dy=-(5(x^2)e^x+3xe^x +3e^x)/(x.e^x)^2