Find #d/dx arctan(sqrt(x)+sqrt(a))#?
1 Answer
Sep 29, 2017
# d/dx(sqrt(x)+sqrt(a)) = 1/(2sqrt(x)(1+(sqrt(x)+sqrt(a))^2))#
Explanation:
Using:
# d/dx(arctanx) = 1/(1+x^2)# ,
and applying the chain rule, We have:
# d/dx arctan(sqrt(x)+sqrt(a)) = 1/(1+(sqrt(x)+sqrt(a))^2) d/dx(sqrt(x)+sqrt(a)) #
# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 1/(1+(sqrt(x)+sqrt(a))^2) (1/2x^(-1/2))#
# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 1/(1+(sqrt(x)+sqrt(a))^2) (1/(2sqrt(x)))#
# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 1/(2sqrt(x)(1+(sqrt(x)+sqrt(a))^2))#
