Question

calcular a derivada de cada uma das funcoes f(x)=1n(2x+3)

Answer 1

Vamos lá:

Neste caso devemos aplicar a regra da cadeia, que consiste em diferenciar a função externa no derivado da função interna, vejamos:

$\mathsf{\dfrac{d}{dx}~(ln(2x+3))}}}\\\\\\\\\ \mathsf{f'(x)=\dfrac{1}{(2x+3)}}~\cdot~\mathsf{\dfrac{d}{dx}((2x+3))}}}\\\\\\\\\ \mathsf{f'(x)=\dfrac{1}{(2x+3)}}~\cdot~\mathsf{\bigg(\dfrac{d}{dx}(2x)+\dfrac{d}{dx}(3)\bigg)}}\\\\\\\\ \mathsf{f'(x)=\dfrac{1}{(2x+3)}}~\cdot~\mathsf{\bigg(2\dfrac{d}{dx}(x)+0\bigg)}}}\\\\\\\\ \mathsf{f'(x)=\dfrac{1}{(2x+3)}}~\cdot~\mathsf{(0+2~\cdot~1)}}}\\\\\\\\\ \mathsf{f'(x)=\dfrac{1}{(2x+3)}}~\cdot~\mathsf{2}}}\\\\\\\\ \large\boxed{\boxed{\boxed{\mathsf{f'(x)=\dfrac{2}{2x+3}}}}}}}}}}}}}}}}}}$

Ou seja, a derivada de 1ª ordem de f (x) = ln (2x + 3) é igual a f'(x) = 2/2x+3.

Espero que te ajude. '-'