If y 2x 1 x7 3 What is y Solutiony 2x1x73 Let y uv3 y 3u

If y = (2x- 1 / x+7 )^3. What is y\' ?

y= (2x-1)/(x+7)^3

Let y= (u/v)^3

==> y\' = 3*(u/v)\' (u/v)^2

But (u/v)\' = (u\'v-uv\')/v^2

==> y\' = 3*[(u\'v-uv\')/v^2] *(u/v^2)

= 3*[uu\'v - u^2*v]/v^4

u= 2x-1 ==> u\' = 2

v= x+7 ==> v\' = 1

Now substitute:

==> y\' = 3[2(2x-1)(x+7) - (2x-1)^2 ]/(x+7)^4

= 6(2x^2+13x -7) - (4x^2 -4x + 1)]/(x+7)^4

= (12x^2 + 78x - 42 - 4x^2 + 4x -1)/(x+7)^4

= (8x^2 +82x - 43)/(x+7)^4

==> y\' = (8x^2 + 82x - 43)/(x+7)^4

$If y = (2x- 1 / x+7 )^3. What is y\' ?Solutiony= (2x-1)/(x+7)^3 Let y= (u/v)^3 ==> y\' = 3*(u/v)\' (u/v)^2 But (u/v)\' = (u\'v-uv\')/v^2 ==> y\' = 3*[(u\'$

If y 2x 1 x7 3 What is y Solutiony 2x1x73 Let y uv3 y 3u

Solution

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