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

##### 1 Answer

Jul 24, 2017

#### 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#