Help with calc chain rule. pleaseeee! 10 POINTS ASAPPPP!

find derivative of function.

f(x)= tan^7(sqrt(csc5x))


Please and Thank youuuuu :)

Let r = 5x, s = csc r, t = √s, u = tan t, and v = u^7. Then

dv/du = 7u^6
du/dt = sec^2(t)
dt/ds = 1/(2√s)
ds/dr = -csc r cot r
dr/dx = 5.

By the chain rule,

f'(x) = dv/du • du/dt • dt/ds • ds/dr • dr/dx

= 7u^6 • sec^2(t) • 1/(2√s) • (-csc r cot r) • 5

= 35/2 tan^6(√s) • sec^2(√s) • (csc r)^(-1/2) • (-csc r cot r)

= -35/2 tan^6(√csc r) • sec^2(√csc r) • √csc r • cot r

= -35/2 tan^6(√csc(5x)) • sec^2(√csc(5x)) • √csc(5x) • cot(5x).