What Is the Correct Derivative of 2v in the Context of Differentiation?

[g$up]

Homework Statement

Find the value of the following derivative at x=1:

d/dx(2v/u)

where u(1)=3, u'(1)=-4, v(1)=-2, v'(1)=5

The Attempt at a Solution

Differentiating the equation:

[(u)(2v') - (u')(2v)]/(u^2)

plugging in the values i get 14/9 as the value.


now my question arises from the derivative of 2v. Would it be just 2? or 2v' as v represents a 'complex base' (therefore using the chain rule)??

the question seems simple enough to me as well but i just want to clarify this.

thanks.

 

[tiny-tim]

Welcome to PF!

Hi g$up! Welcome to PF!

… now my question arises from the derivative of 2v. Would it be just 2? or 2v' as v represents a 'complex base' (therefore using the chain rule)??

The derivative (wrt x) of 2v is definitely 2v'.

 

[Mark44]

To expand on what tiny-tim said, d/dv(2v) = 2, but with d/dx(2v) there's a tacit assumption that v is a function of x, so d/dx(2v) = 2dv/dx = 2v'. In this problem, both u and v are assumed to be differentiable functions of x.