Find (d)/(dv)(3v^(3)-3sin v) Answer:

Differentiate 3v^3: Differentiate the term 3v^3 with respect to v. To differentiate 3v^3, we use the power rule which states that the derivative of v^n with respect to v is n*v^(n-1). Therefore, the derivative of 3v^3 is 3*(3)*v^(3-1) = 9v^2.Differentiate -3sin(v): Differentiate the term -3sin(v) with respect to v. The derivative of sin(v) with respect to v is cos(v). Therefore, the derivative of -3sin(v) is -3cos(v).Combine derivatives: Combine the derivatives from Step 1 and Step 2. The derivative of the entire function 3v^3 - 3sin(v) with respect to v is the sum of the derivatives of its terms, which is 9v^2 - 3cos(v).

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Find $\frac{d}{d v}\left(3 v^{3}-3 \sin v\right)$ $\newline$ Answer:

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Q. Find

\frac{d}{d v}\left(3 v^{3}-3 \sin v\right)

\newline

Answer:

Differentiate $3v^3$ : Differentiate the term $3v^3$ with respect to $v$ . To differentiate $3v^3$ , we use the power rule which states that the derivative of $v^n$ with respect to $v$ is $n\cdot v^{(n-1)}$ . Therefore, the derivative of $3v^3$ is $3\cdot(3)\cdot v^{(3-1)} = 9v^2$ .
Differentiate $-3\sin(v)$ : Differentiate the term $-3\sin(v)$ with respect to $v$ . The derivative of $\sin(v)$ with respect to $v$ is $\cos(v)$ . Therefore, the derivative of $-3\sin(v)$ is $-3\cos(v)$ .
Combine derivatives: Combine the derivatives from Step $1$ and Step $2$ . $\newline$ The derivative of the entire function $3v^3 - 3\sin(v)$ with respect to $v$ is the sum of the derivatives of its terms, which is $9v^2 - 3\cos(v)$ .