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

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

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

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Algebra 2

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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 $16p^3 - 4\cos(p)$ .