How do you differentiate f(x)=csc(sqrt(2x)) f(x)=csc(√2x) using the chain rule?
1 Answer
Jan 2, 2016
Explanation:
According to the chain rule,
d/dx(cscu)=-u'cscucotu
Thus,
f'(x)=d/dx(csc(sqrt(2x)))=-csc(sqrt(2x))cot(sqrt(2x))*d/dx(sqrt(2x))
To find
d/dx(sqrtu)=1/(2sqrtu)*u'
So,
d/dx(sqrt(2x))=1/(2sqrt(2x))*2=1/(sqrt(2x)
Plug this back in to find
f'(x)=(-csc(sqrt(2x))cot(sqrt(2x)))/(sqrt(2x))