Find (d)/(dy)(3y^(4)-3cos y) Answer:

Differentiate y^(4): Differentiate the term 3y^(4) with respect to y. To differentiate 3y^(4), we use the power rule, which states that the derivative of y^n with respect to y is n*y^(n-1). Therefore, the derivative of 3y^(4) is 4*3y^(4-1) = 12y^(3).Differentiate -3cos(y): Differentiate the term -3cos(y) with respect to y. To differentiate -3cos(y), we use the derivative rule for cosine, which states that the derivative of cos(y) with respect to y is -sin(y). Therefore, the derivative of -3cos(y) is -3*(-sin(y)) = 3sin(y).Combine Results: Combine the results from Step 1 and Step 2. The derivative of the entire function 3y^(4)-3cos(y) with respect to y is the sum of the derivatives of its terms. Therefore, the derivative is 12y^(3) + 3sin(y).

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Find $\frac{d}{d y}\left(3 y^{4}-3 \cos y\right)$ $\newline$ Answer:

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Q. Find

\frac{d}{d y}\left(3 y^{4}-3 \cos y\right)

\newline

Answer:

Differentiate $y^{4}$ : Differentiate the term $3y^{4}$ with respect to $y$ . To differentiate $3y^{4}$ , we use the power rule, which states that the derivative of $y^n$ with respect to $y$ is $n\cdot y^{(n-1)}$ . Therefore, the derivative of $3y^{4}$ is $4\cdot 3y^{(4-1)} = 12y^{3}$ .
Differentiate $-3\cos(y)$ : Differentiate the term $-3\cos(y)$ with respect to $y$ . To differentiate $-3\cos(y)$ , we use the derivative rule for cosine, which states that the derivative of $\cos(y)$ with respect to $y$ is $-\sin(y)$ . Therefore, the derivative of $-3\cos(y)$ is $-3*(-\sin(y)) = 3\sin(y)$ .
Combine Results: Combine the results from Step $1$ and Step $2$ . $\newline$ The derivative of the entire function $3y^{4}-3\cos(y)$ with respect to $y$ is the sum of the derivatives of its terms. Therefore, the derivative is $12y^{3} + 3\sin(y)$ .