How do you find the derivative of #sqrt(4+x^2)#?

1 Answer
Ratnaker Mehta
Jul 12, 2016

Reqd. Deri. #=x/(sqrt(4+x^2)).#

Explanation:

Let #y=sqrt(4+x^2), = sqrt t.........(1)#, where #t=4+x^2....(2)#

Thus, #y# is a fun. of #t#, #t# that of #x#.

In such cases, the Chain Rule is to be applied to get the reqd. deri.

Reqd. Deri. #=dy/dx=dy/dt*dt/dx#
#=d/dt(sqrtt)*d/dx(4+x^2)#............[#(1) and (2)#]
#=1/(2sqrtt)(2x)=x/sqrtt=x/(sqrt(4+x^2)).#

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