Find the derivative of h(x)=(4x^3-7x+8)/x

Gardiolo0j 2022-09-29 Answered
Find the derivative of h = ( x ) = 4 x 3 7 x + 8 x
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Answers (1)

Colin Dougherty
Answered 2022-09-30 Author has 8 answers
Step 1
Given: h = ( x ) = 4 x 3 7 x + 8 x
To find- The derivative of the above function.
Identity Used- Using the derivative of the quotient function as
d d x ( f ( x ) g ( x ) ) = g ( x ) × f ( x ) f ( x ) × g ( x ) g ( x ) 2 , where ,br.f(x) and g(x) are the function of x.
Step 2
Explanation- Rewrite the given expression,
h ( x ) = 4 x 3 7 x + 8 x
Using the derivative of the quotient function, differentiating the above expression w.r.t. x, we get,
h ( x ) = x ( 12 x 2 7 ) ( 4 x 3 7 x + 8 ) 1 x 2
= 12 x 3 7 x 4 x 3 + 7 x 8 x 2
= 8 x 3 8 x 2
= 8 ( x 3 1 ) x 2
So, the derivative of the above function is
h ( x ) = 8 ( x 3 1 ) x 2
Answer- the derivative of the function
4 x 3 7 x + 8 x is h ( x ) = 8 ( x 3 1 ) x 2
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