Find (d)/(dv)(4v^(5)-cos v) Answer:

Apply Power Rule: To find the derivative of the function 4v^(5) - cos(v) with respect to v, we need to apply the power rule to the term 4v^(5) and the derivative of the cosine function to the term -cos(v).Derivative of Cosine: The power rule states that the derivative of v^n with respect to v is n*v^(n-1). Applying this to 4v^(5), we get 5*4v^(4) or 20v^(4).Combine Derivatives: The derivative of -cos(v) with respect to v is sin(v), but since we have a negative sign, it becomes -sin(v).Check for Errors: Combining the derivatives of both terms, we get the derivative of the entire function: 20v^(4) - sin(v).We check for any mathematical errors in the differentiation process. The power rule was applied correctly, and the derivative of the cosine function was also correctly determined.

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Find $\frac{d}{d v}\left(4 v^{5}-\cos v\right)$ $\newline$ Answer:

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Q. Find

\frac{d}{d v}\left(4 v^{5}-\cos v\right)

\newline

Answer:

Apply Power Rule: To find the derivative of the function $4v^{5} - \cos(v)$ with respect to $v$ , we need to apply the power rule to the term $4v^{5}$ and the derivative of the cosine function to the term $-\cos(v)$ .
Derivative of Cosine: The power rule states that the derivative of $v^n$ with respect to $v$ is $n*v^{(n-1)}$ . Applying this to $4v^{5}$ , we get $5*4v^{4}$ or $20v^{4}$ .
Combine Derivatives: The derivative of $-\cos(v)$ with respect to $v$ is $\sin(v)$ , but since we have a negative sign, it becomes $-\sin(v)$ .
Check for Errors: Combining the derivatives of both terms, we get the derivative of the entire function: $20v^{4} - \sin(v)$ .
Check for Errors: Combining the derivatives of both terms, we get the derivative of the entire function: $20v^{4} - \sin(v)$ .We check for any mathematical errors in the differentiation process. The power rule was applied correctly, and the derivative of the cosine function was also correctly determined.