# What is the instantaneous rate of change of #f(x)=ln(4x^2-6) # at #x=-2 #?

##### 1 Answer

Apr 5, 2016

#### Explanation:

This is the value of f'(-2)

differentiate using the

#color(blue)" chain rule " #

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

#"-----------------------------------------------------------------"# f(g(x))

# = ln(4x^2 - 6) rArr f'(g(x)) = 1/(4x^2 - 6) # and g(x)

#=4x^2 - 6 rArr g'(x) = 8x #

#"----------------------------------------------------------------"#

#rArr f'(x) = 1/(4x^2 - 6) xx 8x = (8x)/(4x^2 - 6)#

#rArr f'(-2) = (-16)/(16-6) = -8/5 #