Question

Найти производную функции

1) y=e-ln x

2) y=ln(10-5x)

3) y=3-4ln (1-x)

4) y=ln(1/x)

5) y=1-3^x

Answer 1

1.

$\y=e-ln x\ y'=-frac{1}{x}$

 

2.

$\y=ln(10-5x)\ y'=frac{1}{10-5x}cdot-5\ y'=frac{-5}{10-5x}\ y'=frac{-5}{5(2-x)}\ y'=frac{1}{x-2}$

 

3.

$\y=3-4ln (1-x)\ y'=-4cdotfrac{1}{1-x}cdot(-1)\ y'=-frac{4}{x-1}$

 

4.

$\y=ln frac{1}{x}\ y'=frac{1}{frac{1}{x}}cdot(-frac{1}{x^2})\ y'=-frac{x}{x^2}\ y'=-frac{1}{x}$

 

5.

$\y=1-3^x\ y'=-3^x ln 3$