Why derivative of d(2at)/dt is 2a?
I was studying about parametric differentiation and in the book I saw that the derivative of the following below is 2a and I don't understand why implicit differentiation isn't applied here..
#d/dt (2at)# = 2a * 1 = 2a
Isn't it supposed to be:
#d/dt(2at)#
=#2 ( d/dt (a) * t + d/dt (t) * a )#
=#2 ( t (da)/dt+ a )#
I was studying about parametric differentiation and in the book I saw that the derivative of the following below is 2a and I don't understand why implicit differentiation isn't applied here..
Isn't it supposed to be:
=
=
1 Answer
Because
Using the limit definition of derivative, if
On the other hand if
In this case since in general
and if
then:
which is the result of the product rule.