I rewrote the quesion

Question

y = sqrt (4 + sin 10x)

Answer 1

change it to
y = (4+sin10x)^(1/2)
so
dy/dx = (1/2)(4+sin10x)^(-1/2)(10cos10x)
= 5cos10x /(4+sin10x)^(1/2)
= 5cos10x /√(4+sin10x)