Question

Aplicando las reglas de la derivación, calculara las siguientes derivadas
1. f(x)=ln⁡(x)/x
2. f(x)=x^2∙2^x
3. f (t)=(t^2+1)∙(t^3+t^2+1)

Answer 1

1. f'(x)=((1/x)*(x)-ln(x)(-1/x²))/x²
f'(x)=((1+ln(x)/x²))/x²
f'(x)=(x²+ln(x))/x⁴

2. f(x)=x².2ˣ
f'(x)=2x(2ˣ)+x²(2ˣln(2))
f'(x)=2ˣ⁺¹(x)+2ˣx²ln(2)

3.f (t)=(t²+1)∙(t³+t²+1)
f'(t)=(2t)((t³+t²+1)+(t²+1)(3t²+2t)