Find (d)/(dp)(3p^(2)+4cos p) Answer:

Differentiate 3p^2: Differentiate the term 3p^2 with respect to p. To differentiate 3p^2, we use the power rule, which states that the derivative of p^n with respect to p is n*p^(n-1). Therefore, the derivative of 3p^2 is 2*3*p^(2-1) = 6p.Differentiate 4cos(p): Differentiate the term 4cos(p) with respect to p. To differentiate 4cos(p), we use the chain rule and the fact that the derivative of cos(p) with respect to p is -sin(p). Therefore, the derivative of 4cos(p) is 4*(-sin(p)) = -4sin(p).Combine derivatives: Combine the derivatives from Step 1 and Step 2. The derivative of the entire function 3p^2 + 4cos(p) with respect to p is the sum of the derivatives of its terms, which is 6p - 4sin(p).

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Find $\frac{d}{d p}\left(3 p^{2}+4 \cos p\right)$ $\newline$ Answer:

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Q. Find

\frac{d}{d p}\left(3 p^{2}+4 \cos p\right)

\newline

Answer:

Differentiate $3p^2$ : Differentiate the term $3p^2$ with respect to $p$ . To differentiate $3p^2$ , we use the power rule, which states that the derivative of $p^n$ with respect to $p$ is $n\cdot p^{(n-1)}$ . Therefore, the derivative of $3p^2$ is $2\cdot 3\cdot p^{(2-1)} = 6p$ .
Differentiate $4\cos(p)$ : Differentiate the term $4\cos(p)$ with respect to $p$ . To differentiate $4\cos(p)$ , we use the chain rule and the fact that the derivative of $\cos(p)$ with respect to $p$ is $-\sin(p)$ . Therefore, the derivative of $4\cos(p)$ is $4*(-\sin(p)) = -4\sin(p)$ .
Combine derivatives: Combine the derivatives from Step $1$ and Step $2$ . $\newline$ The derivative of the entire function $3p^2 + 4\cos(p)$ with respect to $p$ is the sum of the derivatives of its terms, which is $6p - 4\sin(p)$ .