Question

Usando diretamente o cálculo de limite encontre as derivadas das seguintes funções:
a) f(x)=3x-1

Answer 1

$\boxed{\mathrm{f'(x)=\lim_{h\to0}\dfrac{f(x+h)-f(x)}{h}}}\\\\\\ \mathrm{f(x)=3x-1\ \to\ \mathrm{f'(x)=\lim_{h\to0}\dfrac{3(x+h)-1-(3x-1)}{h}}=}\\\\ \mathrm{=\lim_{h\to0}\dfrac{3x+3h-1-3x+1}{h}=\lim_{h\to0}\dfrac{3h}{h}=\lim_{h\to0}3=\boxed{\mathbf{3}}}$