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Find
(d)/(dp)(4p^(4)-4sin p)
Answer:

Find $\frac{d}{d p}\left(4 p^{4}-4 \sin p\right)$ $\newline$ Answer:

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Simplify radical expressions with root inside the root

Full solution

Q. Find

\frac{d}{d p}\left(4 p^{4}-4 \sin p\right)

\newline

Answer:

Identify function: Identify the function to differentiate. $\newline$ We are given the function $f(p) = 4p^4 - 4\sin(p)$ , and we need to find its derivative with respect to $p$ .
Apply power rule: Apply the power rule to the first term. $\newline$ The power rule states that the derivative of $p^n$ with respect to $p$ is $n*p^{(n-1)}$ . Therefore, the derivative of $4p^4$ with respect to $p$ is $4 \times 4p^{(4-1)} = 16p^3$ .
Apply sine derivative rule: Apply the derivative rule for the sine function to the second term. $\newline$ The derivative of $\sin(p)$ with respect to $p$ is $\cos(p)$ . Therefore, the derivative of $-4\sin(p)$ with respect to $p$ is $-4\cos(p)$ .
Combine derivatives: Combine the derivatives of the terms. $\newline$ The derivative of the function $f(p) = 4p^4 - 4\sin(p)$ with respect to $p$ is the sum of the derivatives of its terms, which is $16p^3 - 4\cos(p)$ .
Write final answer: Write the final answer. $\newline$ The derivative of the function $4p^4 - 4\sin(p)$ with respect to $p$ is $16p^3 - 4\cos(p)$ .

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