Questions: Find (f^prime(x)). (f(x)=(4 x^5+8)^3) (f^prime(x)=square)

Find (f^prime(x)). (f(x)=(4 x^5+8)^3) (f^prime(x)=square)
Transcript text: Find $f^{\prime}(x)$. \[ \begin{array}{l} f(x)=\left(4 x^{5}+8\right)^{3} \\ f^{\prime}(x)=\square \end{array} \]
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Solution

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Solution Steps

Step 1: Identify the function and the order of the derivative to be found

We are given the function \(f(x) = (4*x^5 + 8)^3\) and asked to find its 1th derivative.

Step 2: Apply the differentiation rule

Since \(n=1\), we use the chain rule: \((f(g(x)))' = m \cdot (g(x))^2 \cdot g'(x)\).

Step 3: Calculate the derivative

The 1th derivative of the function is calculated as: \(60 x^{4} \left(4 x^{5} + 8\right)^{2}\).

Final Answer:

The 1th derivative of the function \(f(x) = (4*x^5 + 8)^3\) is \(60 x^{4} \left(4 x^{5} + 8\right)^{2}\).

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