Derivadas: División - Soluciones
Solución 1
\[f(x) = \frac{x}{e^x}\]
\[f'(x) = \boxed{\frac{1-x}{e^x}}\]
\[f'(x) = \boxed{\frac{1-x}{e^x}}\]
Solución 2
\[f(x) = \frac{x}{\sin(x)}\]
\[f'(x) = \boxed{\frac{\sin(x) - x\cos(x)}{\sin^2(x)}}\]
\[f'(x) = \boxed{\frac{\sin(x) - x\cos(x)}{\sin^2(x)}}\]
Solución 3
\[f(x) = \frac{x^2}{e^x}\]
\[f'(x) = \boxed{\frac{x(2-x)}{e^x}}\]
\[f'(x) = \boxed{\frac{x(2-x)}{e^x}}\]
Solución 4
\[f(x) = \frac{\sin(x)}{\cos(x)}\]
\[f'(x) = \boxed{\frac{1}{\cos^2(x)}}\]
\[f'(x) = \boxed{\frac{1}{\cos^2(x)}}\]