Home > Calculus > Solving Separable Differential Equations

How do you find the differential #dy# of the function #y=(x+1)/(2x-1)#?

Answer 1

Charles Anctil

The differential of #y# is the derivative of the function times the differential of #x#

#dy = ((1)(2x-1)-(x+1)(2))/(2x-1) dx#

# = (-3)/(2x-1) dx#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Paisley Johnson

To find the differential ( dy ) of the function ( y = \frac{{x + 1}}{{2x - 1}} ), you can differentiate the function with respect to ( x ) using the quotient rule. The quotient rule states that if you have a function of the form ( \frac{{f(x)}}{{g(x)}} ), its derivative is given by:

[ \frac{{d}}{{dx}}\left(\frac{{f(x)}}{{g(x)}}\right) = \frac{{f'(x)g(x) - f(x)g'(x)}}{{[g(x)]^2}} ]

Apply this rule to the function ( y = \frac{{x + 1}}{{2x - 1}} ) to find ( dy ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.