The discussion centers on the differentiation of the equation xy=c² using implicit differentiation and explicit differentiation. When applying implicit differentiation, the result is dy/dx = -y/x. Conversely, when the equation is rewritten as y = c²/x and differentiated explicitly, the result is dy/dx = -c²/x². Both forms yield equivalent results, as -y/x simplifies to -c²/x², confirming that the differentiation methods are consistent and correct.
PREREQUISITESStudents and educators in mathematics, particularly those studying calculus, as well as anyone interested in understanding the nuances of differentiation methods.
vikcool812 said:I have a relation xy=c2 , if i apply implicit differentiation to both sides i get dy/dx =-y/x , but if i write the same thing as y=c2/x , then dy/dx comes out to be -c2/x2 , what's going wrong ?
Nothing since -y/x = -c²/x2 !vikcool812 said:I have a relation xy=c2 , if i apply implicit differentiation to both sides i get dy/dx =-y/x , but if i write the same thing as y=c2/x , then dy/dx comes out to be -c2/x2 , what's going wrong ?