Question #e7a28

1 Answer
Jan 19, 2018

y'=cos(sqrtx)/(2sqrtx)

Explanation:

Given: y=sin(sqrtx)

Using the chain rule:

y'=(f(g(x))'=f'(g(x))*g'(x)

Let:

f(x)=sin(x)=>f'(x)=cos(x)

g(x)=sqrtx=>g'(x)=x^(1/2)->1/2x^(-1/2)=1/(2sqrtx)

So

y'=cos(sqrtx)*1/(2sqrtx)

y'=cos(sqrtx)/(2sqrtx)