1. Tardigrade
  2. Question
  3. Mathematics
  4. Let u( x ) and v( x ) are differentiable functions such that ( u ( x )/ v ( x ))=7. If ( u prime( x )/ v prime( x ))= p and (( u ( x )/ v ( x ))) prime= q, then ( p + q / p - q ) has the value equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $u( x )$ and $v( x )$ are differentiable functions such that $\frac{ u ( x )}{ v ( x )}=7$. If $\frac{ u ^{\prime}( x )}{ v ^{\prime}( x )}= p$ and $\left(\frac{ u ( x )}{ v ( x )}\right)^{\prime}= q$, then $\frac{ p + q }{ p - q }$ has the value equal to

Continuity and Differentiability

Solution:

$ u ( x )=7 v ( x ) \Rightarrow u ^{\prime}( x )=7 v ^{\prime}( x ) \Rightarrow p =7 \text { (given) }$
again $\frac{u(x)}{v(x)}=7 \Rightarrow\left(\frac{u(x)}{v(x)}\right)^{\prime}=0 \Rightarrow q=0$; now $\frac{p+q}{p-q}=\frac{7+0}{7-0}=1$