Question

Differentiate w. r. t. x. y= log(3x) .

Answer 1

Step-by-step explanation:

• y= log(3x)
• differentiating both side w.r.t. x
• dy/dx = d/dx(log 3x)
• now applying chain rule to solve log 3x as we know that d/dx(logx) =1/x then d/dx( log3x) =1/3x so , by chain rule
• dy/dx = 1/ 3x . d/dx(3x)
• dy/dx = 1/3x . 3 .d/dx(x)
• as we know that derivative of x is 1
• dy/ dx = 1/3x .3 (1)
• hence dy/dx = 1/x

Hope it is helpful

Answer 2

Solution: Let:u=3^x. du/dx=3^x log 3. let:u=log3x=logx/og3. dv/dx= 1/log3 d/dx(logx) =1/log3 1/x =1/1logx. du/dv=(du/dx)/dv/dx=(3^xlog3)/1/xlog3 du/dv=3^.x(log3^2)