Question

Determine a derivada de ordem 3 das funções:

a) f(x) = e^x

b) g(x) = sen(x)

c) h(x) = cos(x)

d) i(x) = ln(x)

Answer 1

Explicação passo-a-passo:

a)A deriva de $e^{x}$ é o próprio  $e^{x}$ .

$f(x)= e^{x} \\\\f'(x)= e^{x} \\\\f''(x)= e^{x} \\\\\boxed{\boxed{f'''(x)= e^{x} }}$

b)

$g(x)=sen(x)\\\\g'(x)=cos(x)\\\\g''(x)=-sen(x)\\\\\boxed{\boxed{g'''(x)=-cos(x)}}$

c)

$h(x)=cos(x)\\\\h'(x)=-sen(x)\\\\h''(x)=-cos(x)\\\\h'''(x)=-(-sen(x))\\\\\boxed{\boxed{h'''(x)=cos(x)}}$

d)

$i(x)=\ln(x)\\\\i'(x)=\dfrac{1}{x}\\\\ i''(x)=\dfrac{d}{dx}.\bigg(\dfrac{1}{x}\bigg)=\dfrac{d}{dx}.x^{-1} \\\\i''(x)=-1.xx^{-1-1}\\\\i''=-x^{-2}\\\\i'''(x)=(-2).(-x^{-2-1} )\\\\i'''(x)=2x^{-3}\\\\\boxed{\boxed{i'''(x)=\dfrac{2}{x^{3} } }}$