Dezembro 23, 2019

por Cindelyn

Como você diferencia $y = {log x}^{2}$ $y = log x ^ 2$ ?

Responda:

$\frac{d y}{d x} = \frac{2}{x}$ $dy/dx=2/x$

Explicação:

There are 2 possible approaches.

$Approach 1$ $color(blue)"Approach 1"$

differentiate using the $chain rule$ $color(blue)"chain rule"$

$color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(log(f(x)))=1/(f(x)).f'(x))color(white)(2/2)|)))$

$y=log(x^2)$

$rArrdy/dx=1/x^2.d/dx(x^2)=1/x^2 xx2x=2/x$

$color(blue)"Approach 2"$

Using the $color(blue)"law of logs"$ then differentiate.

$color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(logx^n=nlogx)color(white)(2/2)|)))$

$y=logx^2=2logx$

$rArrdy/dx=2xx 1/x=2/x$