`y = cos(sqrt(sin(tan(x)))` Find the derivative of the function.

Expert Answers
hkj1385 eNotes educator| Certified Educator

Notes:- 1) If y = cos(ax) ; then dy/dx = -a*sin(ax) ; where 'a' = constant

2) If y = tan(ax) ; then dy/dx = a*sec^2(ax)

3) If y = sin(ax) ; then dy/dx = a*cos(ax) ; where 'a' = constant

4) If y = sqrt(x) ; then dy/dx = 1/{2*sqrt(x)}

5) If a function to be differentiated contains sub-functions, then the differentiation of the last function is done first and so on

Now,

given , y = cos[sqrt{sin(tanx)}]

thus, 

dy/dx=`y' = -sec^2(x)*{cos(tanx)}*sin[sqrt{sin(tanx)}]/[2*sqrt{sin(tanx)}]`