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Calculats the derivative of the function. g(x)=(x^(2)-7x-1)^(-9)

User Wnvko
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1 Answer

1 vote

Answer:


(-9(2x -7))/((x^2 - 7x - 1)^(10))

Explanation:

1. To derive a function we use the power rule, it states:

The derivative of
x^n is
nx^(n-1)

2. Furthermore since this function has x in brackets to a power we need to use the chain rule


(dy)/(dx) =
(du)/(dx) x
(dy)/(du)

3. For this equation let

u =
x^2 - 7x - 1

y =
u^(-9)

lets differentiate u first using the power rule


(du)/(dx) = 2x -7


(dy)/(du) =
-9u^{-10

a negative exponent is simply
(1)/(x^n) therefore


-9u^{-10 =
(-9)/(u^(10))

now we do
(du)/(dx) x
(dy)/(du)


(-9)/(u^(10)) x 2x -7 =


(-9(2x -7))/(u^(10))

3. Now we replace the u with its original value


(-9(2x -7))/((x^2 - 7x - 1)^(10))

User W A Carnegie
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8.2k points