Question

Ajuda com derivadas, por favor

Answer 1

Resposta:

Regrado TOMBO ==>f(x)=a*x^n  ==>f'(x)=a*n*x^(n-1)

f(x)=x ==>f'(x)=1*x^(1-1) =1*x^0 =1

f(x)=ln[h(x)] ==>f'(x)=h(x)'/ln[h(x)]

f(x)=e^[h(x)]  ==>f'(x)=h(x)' * e^[h(x)]

f(x)=cos(h(x)) ==>f'(x)=h(x)'*[-sen(h(x)]

1)

f(x)=3x⁵+(1/3)*x⁴+x+2

f'(x)=15x^4+(4/3)*x³+1

2)

x²+1/x²+x^(1/2)

f'(x)= 2x - 2*x⁻³ +1/2√x

f'(x)= 2x - 2/x³+1/2√x

3)

f(x)=x³+ln(x)

f'(x)=3x²+1/x

4)

f(x)=2*e^(x)+cos(x)

f'(x)=2*e^x -sen(x)