# How do you differentiate #f(x)= e^x/(x-7 )# using the quotient rule?

Quotient rule states that

Application to the given examples yields

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

To differentiate ( f(x) = \frac{e^x}{x - 7} ) using the quotient rule:

- Let ( u = e^x ) and ( v = x - 7 ).
- Find ( u' ) and ( v' ).
- ( u' = e^x ) (since the derivative of ( e^x ) is ( e^x ))
- ( v' = 1 ) (since the derivative of ( x - 7 ) is ( 1 ))

- Apply the quotient rule: [ \frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2} ]
- Substitute ( u' ), ( v' ), ( u ), and ( v ) into the formula: [ \frac{d}{dx}\left(\frac{e^x}{x - 7}\right) = \frac{(e^x)(x - 7) - (e^x)(1)}{(x - 7)^2} ]
- Simplify the expression: [ \frac{d}{dx}\left(\frac{e^x}{x - 7}\right) = \frac{e^x(x - 7) - e^x}{(x - 7)^2} ]
- Further simplification may be possible, but this is the result of differentiating ( f(x) ) using the quotient rule.

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

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7