If #f(x) =csc^3(x/4) # and #g(x) = sqrt(x^3+3 #, what is #f'(g(x)) #?

1 Answer
Apr 14, 2016

Answer:

#(f(g(x)))'= 3 csc(1/4 sqrt(x^3+3))^2 xx -csc(1/4 sqrt(x^3+3))cot(1/4 sqrt(x^3+3)) xx1/(8sqrt(x^3+3)) xx3x^2#

Explanation:

#f(g(x))=csc^3(1/4 sqrt(x^3+3))#

#(f(g(x)))'=f'g(x) xxg'(x)#

#(f(g(x)))'= 3 csc(1/4 sqrt(x^3+3))^2 xx -csc(1/4 sqrt(x^3+3))cot(1/4 sqrt(x^3+3)) xx1/(8sqrt(x^3+3)) xx3x^2#