How do you differentiate #f(x)=(2x+3)/6# using the quotient rule?
here
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate ( f(x) = \frac{2x + 3}{6} ) using the quotient rule, you can follow these steps:

Identify ( u(x) ) as the numerator ( 2x + 3 ) and ( v(x) ) as the denominator ( 6 ).

Apply the quotient rule: ( f'(x) = \frac{v(x)u'(x)  u(x)v'(x)}{[v(x)]^2} ).

Calculate ( u'(x) ) and ( v'(x) ), which are the derivatives of the numerator and denominator, respectively.
 ( u'(x) = 2 ) (derivative of ( 2x + 3 ))
 ( v'(x) = 0 ) (since the derivative of a constant is zero)

Substitute the values into the quotient rule formula and simplify.
( f'(x) = \frac{6(2)  (2x + 3)(0)}{6^2} )
( f'(x) = \frac{12}{36} = \frac{1}{3} )
Therefore, the derivative of ( f(x) = \frac{2x + 3}{6} ) is ( f'(x) = \frac{1}{3} ).
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate ( f(x) = \frac{2x + 3}{6} ) using the quotient rule, you apply the formula:
[ \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \cdot \frac{du}{dx}  u \cdot \frac{dv}{dx}}{v^2} ]
where ( u = 2x + 3 ) and ( v = 6 ).
First, find ( \frac{du}{dx} ) and ( \frac{dv}{dx} ):
[ \frac{du}{dx} = \frac{d}{dx}(2x + 3) = 2 ]
[ \frac{dv}{dx} = \frac{d}{dx}(6) = 0 ]
Now, substitute into the quotient rule formula:
[ f'(x) = \frac{6 \cdot 2  (2x + 3) \cdot 0}{6^2} ]
[ f'(x) = \frac{12}{36} ]
[ f'(x) = \frac{1}{3} ]
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.
 How do you use implicit differentiation to find #(dy)/(dx)# given #3x^2+3y^2=2#?
 How do you use the chain rule to differentiate #root11(e^(6x))#?
 How do you find the derivative of #y^2=2+xy#?
 How do you differentiate #f(x) = (cosx)/(sinxcosx)# using the quotient rule?
 How do you find the derivative of #q(x) = (8x) ^(2/3)# using the chain rule?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7