How do you differentiate # f(x)=1/sqrt((7-2x^3)# using the chain rule.?

1 Answer
Jim G.
Apr 14, 2016

# (3x^2)/(7 - 2x^3)^(3/2 )#

Explanation:

Using the #color(blue)" chain rule "#

#d/dx [ f(g(x)) ] = f'(g(x)) . g'(x) #

rewrite # 1/(sqrt(7 - 2x^3)) = (7 - 2x^3)^(-1/2) #
#"-----------------------------------------"#

here f(g(x)) #= (7 - 2x^3)^(-1/2)#

#rArr f'(g(x)) = -1/2(7 - 2x^3)^(-3/2) #

and # g(x) = 7 - 2x^3 rArr g'(x) = -6x^2 #
#"----------------------------------------------------------------"#

#rArr f'(x) = -1/2(7 - 2x^3)^(-3/2) xx-6x^2 #

# = (3x^2)/(7 - 2x^3)^(3/2) #

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