Question

Calcule as derivadas da função y= 2 ln x + 2^x + 1

Answer 1

$y = 2.ln(x) + 2^x + 1$


Derivada primeira:

$y' = 0 . ln(x) + 2 . \frac{1}{x} + 2 + 0$

$\boxed{\bold{y' = \frac{2}{x} + 2}}$


Derivada segunda:

$y'' = \frac{0.x - (2.1)}{x^2} + 0$

$\boxed{\bold{y'' = \frac{-2}{x^2}}}$


Derivada terceira:

$y''' = \frac{0 . x^2 - (-2.2x)}{(x^2)^2}$

$y''' = \frac{- (-4x)}{x^4}$

$y''' = \frac{4x}{x^4}$

$\boxed{\bold{y''' = \frac{4}{x^3}}}$