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DiKsa [7]
3 years ago
6

Y=3x^2+6x-7/(x+1)^2 Show that dy/dx = 20/(x+1)^3

Mathematics
1 answer:
fredd [130]3 years ago
3 0
Apply the quotient rule  
d(uv)  =    v du/dx - u dv/dx
  dx           ----------------------
                         v^2

 du/dx  =  6x + 6
 dv/dx   =  2(x + 1)
 v^2 = (x + 1)^4   so we have

dy dx =  (x + 1)^2 .* (6x + 6) - (3x^2 + 6x - 7) * 2(x + 1)   /  (x + 1)^4

         =   (x + 1) [(6(x + 1)^2 - 2(3x^2 + 6x - 7) ]  / (x + 1)^4

         =  (x^2 + 12x +6 - 6x^2  - 12x + 14 ) / (x + 1)^3  

        =  20 / (x + 1)^3   Answer
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Answer:

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Step-by-step explanation:

h and k are the vertex coordinates

Substitute them in the vertex form equation:

f(x) = a(x − 2)^2 + 3

Calculate "a" by replacing "f(x)" with -7 and "x" with 1:

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Simplify:

-7 = a(1 − 2)^2 + 3

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Replace a to get the final vertex form equation:

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Convert to standard form:

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Expand using binomial theorem:

y = -10(x^2 − 4x + 4) + 3

Simplify:

y = -10x^2 + 40x - 40 + 3

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