Question

If f(x) = `sqrt(7*g(x) - 3)`, g(3) = 4 and g'(3) = 5, find f'(3).

Answer 1

f(x) = `sqrt(7*g(x) - 3)`

Differentiating w.r.t. x, we get

f'(x) = `d/dx [sqrt(7*g(x) - 3)]`

= `1/(2sqrt(7*g(x) - 3)) * d/dx [7*g(x) - 3]`

= `1/(2sqrt(7*g(x) - 3)) xx [7*g^'(x) - 0]`

∴ f'(x) = `(7*g^' (x))/(2sqrt(7*g(x) - 3))`

∴ f'(3) = `(7*g^' (3))/(2sqrt(7*g(3) - 3))`  ...[∵ g(3) = 4 and g'(3) = 5]

= `(7(5))/(2sqrt(7(4) - 3))`

= `35/(2sqrt(25))`

= `35/10`

∴ f'(3) = `7/2`