Question

Find f '(x) for f of x equals the square root of the quantity sine of 8 times x

See attached for the problem and answers

Answer 1

neato

write √sin(8x) as
`(sin(8x))^(1)/(2)`
then use the power rule
remember

`(dy)/(dx)x^m=mx^(m-1)`
and the chain rule

`(dy)/(dx)f(g(x))=f'(g(x))g'(x)`
and derivitive of sin(x)=cos(x)


so

`(dy)/(dx) √(sin(8x))`=

`(dy)/(dx) (sin(8x))^(1)/(2)`=

`(1)/(2)(sin(8x))^(-1)/(2)(dy)/(dx)sin(8x)`=

`(1)/(2√(sin(8x)))cos(8x)(dy)/(dx)8x`=

`(8cos(8x))/(2√(sin(8x)))`=

`(4cos(8x))/(√(sin(8x)))`=

answer is 2nd option