00:01
Okay, in this question, a function y equals to 3x plus 2 raised to the power 4 and 5x minus 1 raise to the power 2 is given and we have to use logarithmic differentiation to find out the derivative of the function.
00:14
Okay, so we will use natural logarithm both side of the equation and it will be lny equals to ln and 3x plus 2 raise to the power 4 and dot 5x minus 1 raise to the power 2.
00:25
Okay, and we can say it will be lna dot b that can be written.
00:30
As lna a plus ln b using the law of logarithm so it will be l n y equals to ln a that is 3 plus 3x plus 2 whole raise to the power 4 plus ln b that is ln 5x minus 1 raised to the power 2 okay and now ln a raised to the power b that can be written as b lna a okay this power comes before the logarithm l n y it will be 4 ln 3x plus 2 plus it will be 2 ln 5x minus 1 okay okay and now we will use the logarithmic differentiation.
01:03
So we will differentiate both of the side and differentiation of l and y.
01:06
It will be y dash by y.
01:09
And the right hand side it will be 4 divided by 3x plus 2.
01:13
Dot using the chain rule differentiation of 3x plus 2 it will be 3.
01:17
Plus 2 and differentiation of ln 5x minus 1.
01:21
It will be 1 divided by 5x minus 1.
01:24
Dot differentiation of this 5x minus 1 it will be 5.
01:27
Okay...