Given the function f(x)=(x^(2)-8x+9)^(5), find f^(')(x) in any form. Answer: f^(')(x)=

Identify Functions: First, let's identify the outer function and the inner function. The outer function is g(u)=u^5 and the inner function is u(x)=x^2-8x+9. We will need to find the derivative of both functions.Derivative of Outer Function: The derivative of the outer function g(u)=u^5 with respect to u is g'(u)=5u^4.Derivative of Inner Function: The derivative of the inner function u(x)=x^2-8x+9 with respect to x is u'(x)=2x-8.Apply Chain Rule: Now, we apply the chain rule. The derivative of f(x) with respect to x is f'(x)=g'(u(x)) * u'(x). Substituting the derivatives we found, we get f'(x)=5(u(x))^4 * (2x-8).Substitute Derivatives: Substitute u(x) back into the equation with its original expression. So, f'(x)=5(x^2-8x+9)^4 * (2x-8).Final Derivative: We have found the derivative of the function f(x) without making any mathematical errors. The derivative is f'(x)=5(x^2-8x+9)^4 * (2x-8).

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Given the function
f(x)=(x^(2)-8x+9)^(5), find
f^(')(x) in any form.
Answer:
f^(')(x)=

Given the function $f(x)=\left(x^{2}-8 x+9\right)^{5}$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$

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Math Problems

Algebra 2

Find the vertex of the transformed function

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Q. Given the function

f(x)=\left(x^{2}-8 x+9\right)^{5}

, find

f^{\prime}(x)

in any form.

\newline

Answer:

f^{\prime}(x)=

Identify Functions: First, let's identify the outer function and the inner function. The outer function is $g(u)=u^5$ and the inner function is $u(x)=x^2-8x+9$ . We will need to find the derivative of both functions.
Derivative of Outer Function: The derivative of the outer function $g(u)=u^5$ with respect to $u$ is $g'(u)=5u^4$ .
Derivative of Inner Function: The derivative of the inner function $u(x)=x^2-8x+9$ with respect to $x$ is $u'(x)=2x-8$ .
Apply Chain Rule: Now, we apply the chain rule. The derivative of $f(x)$ with respect to $x$ is $f'(x)=g'(u(x)) \cdot u'(x)$ . Substituting the derivatives we found, we get $f'(x)=5(u(x))^4 \cdot (2x-8)$ .
Substitute Derivatives: Substitute $u(x)$ back into the equation with its original expression. So, $f'(x)=5(x^2-8x+9)^4 \cdot (2x-8)$ .
Final Derivative: We have found the derivative of the function $f(x)$ without making any mathematical errors. The derivative is $f'(x)=5(x^2-8x+9)^4 \cdot (2x-8)$ .