Home > Calculus > Quotient Rule

How do you differentiate #f(x)=sinx/(x-3)^3# using the quotient rule?

Answer 1

Ezra Adams

#y'=(cos(x)(x-3)-3sin(x))/(x-3)^4#

The Quotient rule allows us to obtain

#y'=(cos(x)(x-3)^3-sin(x)3(x-3)^2)/(x-3)^6# simplifying

#y'=(cos(x)(x-3)-3sin(x))/(x-3)^4#

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

Answer 2

Ezekiel Alexander

To differentiate ( f(x) = \frac{\sin(x)}{(x-3)^3} ) using the quotient rule, follow these steps:

Apply the quotient rule: [ \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{u'v - uv'}{v^2} ]
Identify ( u ) and ( v ): ( u = \sin(x) ) and ( v = (x-3)^3 )
Find ( u' ) and ( v' ): ( u' = \cos(x) ) ( v' = 3(x-3)^2 )
Plug into the quotient rule formula: ( f'(x) = \frac{\cos(x) \cdot (x-3)^3 - \sin(x) \cdot 3(x-3)^2}{(x-3)^6} )
Simplify the expression if needed.

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.