Sin(2x) Türevi

Sin(2x) Türevi Nedir ?

$Sin(2x)$'in türevi, $2.Cos(2x)$'tir.

1. Yol

$y=f(x)=sinx\Rightarrow y^{\prime }=f(x{)}^{\prime }=(sinx{)}^{\prime }=cosx$'tir.

$y=f(x)=sin(u)\Rightarrow y^{\prime }=f(x{)}^{\prime }=sin(u{)}^{\prime }=u^{\prime }.cos(u)$ olur.

$sin(u{)}^{\prime }=u^{\prime }.cos(u)$

$sin(2x{)}^{\prime }=(2x{)}^{\prime }.cos(2x)$

$sin(2x{)}^{\prime }=2.cos(2x)$

2. Yol

$f(x)=g(x).h(x)$ olmak üzere;

$f(x{)}^{\prime }=g(x{)}^{\prime }.h(x)+g(x).h(x{)}^{\prime }$'dir.

$sin(2x)=2.sinx.cosx$'tir.

$sin(2x)=2.(sinx.cosx)$

$sin(2x{)}^{\prime }=(2.(sinx.cosx){)}^{\prime }$

$sin(2x{)}^{\prime }=2^{\prime }.(sinx.cosx)+2.(sinx.cosx{)}^{\prime }$

$sin(2x{)}^{\prime }=0.(sinx.cosx)+2.(sin{x}^{\prime }.cosx+sinx.cos{x}^{\prime })$

$sin(2x{)}^{\prime }=0+2.(cosx.cosx+sinx.(-sinx))$

$sin(2x{)}^{\prime }=2.(co{s}^{2}x-si{n}^{2}x)$

$co{s}^{2}x-si{n}^{2}x=cos(2x)$'tir.

$sin(2x{)}^{\prime }=2.cos(2x)$