Question

Hallar la derivada de la función ㏑ (3x+1 ÷ 2x)

Answer 1

So,

Use the Chain Rule: f(g(x)) --> f'(g(x))g'(x)

But first, rewrite the function using log properties.

$ln(\frac{3x+1}{2x})=ln(3x+1)-ln(2x)$

Now, apply the Chain Rule.

$\frac{dy}{dx}=\frac{3}{3x+1}-\frac{2}{2x}=\frac{3}{3x+1}-\frac{1}{x}$