Mathematics: What is the derivative of

When dividing with exponents you just subtract he exponents so the answer is 5...

What is the derivative of - id5428157, jeffffffff

krys4281

20.01.2022

Answer and Step-by-step explanation:

Greetings!

Let's~answer~your~question!

→ By~quotient~rule,

$y'=\frac{\frac{1}{x}*x~-~In~x*1 }{x^2} =\frac{1-In~x}{x^2}$

→ This~ problem ~can ~also ~be ~solved ~by~ the ~Product~ Rule:

y'=f'(x)~g(x)+f(x)~g(x)

→ The~ original~ function ~can~ also~be~ rewritten~ using ~negative~ exponents:

$f(x)=\frac{In(x)}{x}=In(x)*x^-^1$

$f'(x)=\frac{1}{x} *x^-^1+ln(x)*-1x^-^2$

$f'(x)=\frac{1}{x}*\frac{1}{x}+In(x)*-\frac{1}{x^2}$

$f'(x)=\frac{1}{x^2}-\frac{In(x)}{x^2}$

$f'(x)=\frac{1-In(x)}{x^2}$

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