Home > Calculus > Chain Rule

How do you differentiate #f(y) = e^y /y#?

Answer 1

Evelyn Agard

#(df)/(dy)=e^y((y-1)/y^2)#

We use quotient rule here. According to quotient rule

if #f(x)=(g(x))/(h(x))#

#(df)/(dx)=(h(x)*g'(x)-g(x)*h'(x))/(h(x))^2#

As #f(y)=e^y/y#

#(df)/(dy)=(yxxe^y-e^yxx1)/y^2#

= #e^y((y-1)/y^2)#

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

Answer 2

Evelyn Agard

To differentiate ( f(y) = \frac{e^y}{y} ), you can use the quotient rule. The quotient rule states that if you have a function in the form ( \frac{u}{v} ), where ( u ) and ( v ) are both functions of ( y ), then the derivative is given by ( \frac{u'v - uv'}{v^2} ). Applying this rule to the function ( f(y) = \frac{e^y}{y} ), you get ( f'(y) = \frac{e^y \cdot 1 - e^y \cdot 1}{y^2} = \frac{e^y - e^y}{y^2} = \frac{0}{y^2} = 0 ). So, the derivative of ( f(y) ) with respect to ( y ) is ( 0 ).

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.