Given the function f(x)=-3(4x^(2)-7x)^(5), find f^(')(x) in any form. Answer: f^(')(x)=

Identify Functions: To find the derivative of the function f(x)=-3(4x^(2)-7x)^(5), we will use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.Find Outer Function Derivative: First, let's identify the outer function and the inner function. The outer function is u^5, where u is the inner function. The inner function is 4x^2 - 7x.Find Inner Function Derivative: Now, we will find the derivative of the outer function with respect to the inner function u. The derivative of u^5 with respect to u is 5u^4.Apply Chain Rule: Next, we will find the derivative of the inner function 4x^2 - 7x with respect to x. The derivative of 4x^2 is 8x, and the derivative of -7x is -7. So, the derivative of the inner function is 8x - 7.Simplify Expression: Now, we apply the chain rule. We multiply the derivative of the outer function by the derivative of the inner function. This gives us: f^(')(x) = -3 * 5(4x^2 - 7x)^4 * (8x - 7).Final Answer: Simplify the expression by multiplying the constants and keeping the rest of the expression in its current form. f^(')(x) = -15 * (4x^2 - 7x)^4 * (8x - 7).The final answer is f^(')(x) = -15(4x^2 - 7x)^4(8x - 7).

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Given the function
f(x)=-3(4x^(2)-7x)^(5), find
f^(')(x) in any form.
Answer:
f^(')(x)=

Given the function $f(x)=-3\left(4 x^{2}-7 x\right)^{5}$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$

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Algebra 2

Find the vertex of the transformed function

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Q. Given the function

f(x)=-3\left(4 x^{2}-7 x\right)^{5}

, find

f^{\prime}(x)

in any form.

\newline

Answer:

f^{\prime}(x)=

Identify Functions: To find the derivative of the function $f(x)=-3(4x^{2}-7x)^{5}$ , we will use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.
Find Outer Function Derivative: First, let's identify the outer function and the inner function. The outer function is $u^5$ , where $u$ is the inner function. The inner function is $4x^2 - 7x$ .
Find Inner Function Derivative: Now, we will find the derivative of the outer function with respect to the inner function $u$ . The derivative of $u^5$ with respect to $u$ is $5u^4$ .
Apply Chain Rule: Next, we will find the derivative of the inner function $4x^2 - 7x$ with respect to $x$ . The derivative of $4x^2$ is $8x$ , and the derivative of $-7x$ is $-7$ . So, the derivative of the inner function is $8x - 7$ .
Simplify Expression: Now, we apply the chain rule. We multiply the derivative of the outer function by the derivative of the inner function. This gives us: $f'(x) = -3 \times 5(4x^2 - 7x)^4 \times (8x - 7)$ .
Final Answer: Simplify the expression by multiplying the constants and keeping the rest of the expression in its current form. $f^{\prime}(x) = -15 \times (4x^2 - 7x)^4 \times (8x - 7)$ .
Final Answer: Simplify the expression by multiplying the constants and keeping the rest of the expression in its current form. $f'(x) = -15 \times (4x^2 - 7x)^4 \times (8x - 7)$ .The final answer is $f'(x) = -15(4x^2 - 7x)^4(8x - 7)$ .