Any function f(x) is derivable at x=a, if limh→0+hf(a+h)−f(a)=limh→0−−hf(a−h)−f(a) Given, <br/><br/>f(x)=sin∣x∣⇒f(x)=⎩⎨⎧<br/>sinx<br/>0<br/>−sinxx>0x=0RHD=limh→0−sin∣(0+h)∣−sin(0)x<0<br/><br/>RHD=limh→0hsin((0+h)∣−sin(0)<br/>=limh→0hsinh=1<br/>LHD=limh→0−hsin∣(0−h)∣−sin(0)<br/>=h−sinh=−1<br/>∴LHD=RHD at x=0<br/>∴f(x) is not derivable at x=0.<br/><br/>