How do you implicitly differentiate #22=(y)/(xe^y)#?
In this case,
By signing up, you agree to our Terms of Service and Privacy Policy
To implicitly differentiate ( 22 = \frac{y}{x  e^y} ):
 Start by isolating the numerator and denominator separately.
 Differentiate each term with respect to ( x ) using the quotient rule.
 Apply the chain rule where necessary to differentiate ( e^y ).
 Solve for ( \frac{dy}{dx} ) after differentiation.
The steps are as follows:

( 22(x  e^y) = y )

Differentiate each term:
( 22  22e^y \frac{dy}{dx} = \frac{dy}{dx}(x  e^y) + y )

Apply the chain rule to differentiate ( e^y ):
( \frac{d(e^y)}{dx} = \frac{d(e^y)}{dy} \cdot \frac{dy}{dx} = e^y \frac{dy}{dx} )

Rearrange the terms and solve for ( \frac{dy}{dx} ):
( (x  e^y) \frac{dy}{dx} + 22e^y \frac{dy}{dx} = y  22 )
( \frac{dy}{dx}(x  e^y + 22e^y) = y  22 )
( \frac{dy}{dx} = \frac{y  22}{x  e^y + 22e^y} )
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7