Question #923ff

Question

Question #923ff

1 Answer

Impact of this question

788 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-19T00:41:30

$\frac{tan (2 x) + 2 x {(sec (2 x))}^{2}}{x tan (2 x)}$ $(tan(2x)+2x(sec(2x))^2)/(xtan(2x))$

Explanation:

$\frac{d}{d x} (ln (x tan (2 x)))$ $d/dx(ln(xtan(2x)))$
$= \frac{1}{x tan (2 x)} \cdot \frac{d}{d x} (x tan (2 x))$ $=1/(xtan(2x))*d/dx(xtan(2x))$ (ln(x) derivative and chain rule)

$= \frac{1}{x tan (2 x)} [tan (2 x) \cdot \frac{d}{d x} (x) + x \cdot \frac{d}{d x} (tan (2 x))]$ $=1/(xtan(2x))[tan(2x)*d/dx(x)+x*d/dx(tan(2x))]$ (product rule)

$= \frac{1}{x tan (2 x)} [tan (2 x) \cdot 1 + x \cdot {(sec (2 x))}^{2} \cdot \frac{d}{d x} (2 x)]$ $=1/(xtan(2x))[tan(2x)*1+x*(sec(2x))^2*d/dx(2x)]$ (tanx derivative)

$= \frac{1}{x tan (2 x)} [tan (2 x) + x {(sec (2 x))}^{2} \cdot 2]$ $=1/(xtan(2x))[tan(2x)+x(sec(2x))^2*2]$
$= \frac{tan (2 x) + 2 x {(sec (2 x))}^{2}}{x tan (2 x)}$ $=(tan(2x)+2x(sec(2x))^2)/(xtan(2x))$

(you can do further simplification if you want)

Science

Math

Humanities

... and beyond

Question #923ff

1 Answer

Explanation:

Related questions

Impact of this question