How do you use the limit definition to find the derivative of #f(x)=1/(4x3)#?
So:
and
By signing up, you agree to our Terms of Service and Privacy Policy
To use the limit definition to find the derivative of ( f(x) = \frac{1}{4x  3} ):

Start with the definition of the derivative: [ f'(x) = \lim_{h \to 0} \frac{f(x + h)  f(x)}{h} ]

Substitute the function ( f(x) = \frac{1}{4x  3} ) into the formula: [ f'(x) = \lim_{h \to 0} \frac{\frac{1}{4(x + h)  3}  \frac{1}{4x  3}}{h} ]

Simplify the expression: [ f'(x) = \lim_{h \to 0} \frac{\frac{1}{4x + 4h  3}  \frac{1}{4x  3}}{h} ] [ f'(x) = \lim_{h \to 0} \frac{(4x  3)  (4x + 4h  3)}{h(4x + 4h  3)(4x  3)} ] [ f'(x) = \lim_{h \to 0} \frac{4x  3  4x  4h + 3}{h(4x + 4h  3)(4x  3)} ] [ f'(x) = \lim_{h \to 0} \frac{4h}{h(4x + 4h  3)(4x  3)} ]

Cancel out the ( h ) in the numerator and denominator: [ f'(x) = \lim_{h \to 0} \frac{4}{(4x + 4h  3)(4x  3)} ]

Evaluate the limit as ( h ) approaches 0: [ f'(x) = \frac{4}{(4x  3)(4x  3)} ]

Simplify the expression: [ f'(x) = \frac{4}{(4x  3)^2} ]
Thus, the derivative of ( f(x) = \frac{1}{4x  3} ) is ( f'(x) = \frac{4}{(4x  3)^2} ).
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 find the slope of a tangent line to the graph of the function # f(x)= (2x^2+5x4)/x^2# at x=3?
 What is the relationship between the Average rate of change of a fuction and derivatives?
 How do you find f'(x) using the definition of a derivative for #f(x)=7x^2  3 #?
 What is the equation of the tangent line of #f(x) =e^(3x1)(3x1)# at #x=2#?
 How do you find the equation of the tangent line to the curve #y=sinx+sin^2x# at (0,0)?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7