Question

qual a derivada de e^3x²-x

Answer 1

$\displaystyle \sf \underline{\text{Derivada de uma exponencial}} : \\\\ y=a^{u} \\\\\ y' = a^{u} \cdot u'\cdot \ln (a) \\\\ \text{onde : u {\'e} uma fun{\c c}{\~a}o} \\\\\\ temos : \\\\ y = e^{(3x^2-x)} \\\\ y' = e^{(3x^2-x)} \cdot (3x^2-x)'\cdot \ln e \\\\ \huge\boxed{\sf \ y' = e^{(3x^2-x)}\cdot (6x-1) \ }\checkmark$

comentário :

$\displaystyle \sf y = a^{u} \\\\ \ln y=\ln a^u \\\\ (\ln y)' = (u\cdot \ln a )' \\\\ \frac{y'}{y} = u'\cdot \ln a \\\\ y' = y\cdot u'\cdot \ln a \\\\ \boxed{\sf y' = a^{u}\cdot u'\cdot \ln a}$