How do you use the chain rule to differentiate #root3(4x+9)#?

1 Answer
bp
Dec 8, 2016

#4/3 (4x+9)^(-2/3)#

Explanation:

Consider 4x+9 as some function p of x. Thus #f=p^(1/3)#

Now differentiate f with respect to p and then p with respect to x, to get differential of f w.r.t x. This is the chain rule. It works out as follows:

#(df)/dx= (df)/(dp) * (dp)/dx#

=# 1/3 p^(-2/3) * d/dx (4x+9)#

=#1/3 (4x+9)^(-2/3) * (4)#

=#4/3 (4x+9)^(-2/3)#

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