How to find instantaneous rate of change for sqrt(4t + 6) when t=6?

1 Answer
Jim G.
Jul 24, 2017

f'(t)=2/sqrt30

Explanation:

"the instantaneous value is the derivative of f(t) at x = a"

"differentiate using the "color(blue)"chain rule"

"given "y=f(g(x))" then"

dy/dx=f'(g(x))xxg'(x)larr" chain rule"

f(t)=sqrt(4t+6)=(4t+6)^(1/2)

rArrf'(t)=1/2(4t+6)^(-1/2)xxd/dt(4t+6)

color(white)(rArrf'(t))=2/(4t+6)^(1/2)

rArrf'(6)=2/sqrt30

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