Question

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

Answer 1

`(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)`