Determine the derivative of the function $$ g(x)=(\ln x)^{31} $$

Question

UpStudy AI · Accepted Answer

Find the first order derivative with respect to $$ x $$ for $$ (\ln x)^{31} $$.
Evaluate the derivative by following steps:
- step0: Evaluate the derivative:
  $$\frac{d}{dx}\left(\left(\ln{\left(xight)}ight)^{31}ight)$$
- step1: Use differentiation rules:
  $$\frac{d}{dg}\left(g^{31}ight)	imes \frac{d}{dx}\left(\ln{\left(xight)}ight)$$
- step2: Find the derivative:
  $$31g^{30}	imes \frac{d}{dx}\left(\ln{\left(xight)}ight)$$
- step3: Calculate:
  $$31g^{30}	imes \frac{1}{x}$$
- step4: Substitute back:
  $$31\left(\ln{\left(xight)}ight)^{30}	imes \frac{1}{x}$$
- step5: Multiply the terms:
  $$\frac{31\left(\ln{\left(xight)}ight)^{30}}{x}$$
The derivative of the function $$ g(x) = (\ln x)^{31} $$ with respect to $$ x $$ is $$ \frac{31(\ln x)^{30}}{x} $$.
The derivative of $$ g(x) = (\ln x)^{31} $$ is $$ \frac{31(\ln x)^{30}}{x} $$.

Determine the derivative of the function

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Calculus Questions