Find (d)/(dy)(3y^(2)-sin y) Answer:

Apply Differentiation Rules: To find the derivative of the function 3y^2 - sin(y) with respect to y, we will apply the basic differentiation rules. The power rule for the term 3y^2 and the derivative of the sine function for the term -sin(y).Differentiate 3y^2: Differentiate 3y^2 with respect to y. According to the power rule, the derivative of y^n with respect to y is n*y^(n-1). Therefore, the derivative of 3y^2 is 2*3*y^(2-1) = 6y.Differentiate -sin(y): Differentiate -sin(y) with respect to y. The derivative of sin(y) with respect to y is cos(y), so the derivative of -sin(y) is -cos(y).Combine Derivatives: Combine the derivatives of the two terms to get the derivative of the entire function. The derivative of 3y^2 - sin(y) with respect to y is 6y - cos(y).

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Find $\frac{d}{d y}\left(3 y^{2}-\sin y\right)$ $\newline$ Answer:

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Q. Find

\frac{d}{d y}\left(3 y^{2}-\sin y\right)

\newline

Answer:

Apply Differentiation Rules: To find the derivative of the function $3y^2 - \sin(y)$ with respect to $y$ , we will apply the basic differentiation rules. The power rule for the term $3y^2$ and the derivative of the sine function for the term $-\sin(y)$ .
Differentiate $3y^2$ : Differentiate $3y^2$ with respect to $y$ . According to the power rule, the derivative of $y^n$ with respect to $y$ is $n\cdot y^{(n-1)}$ . Therefore, the derivative of $3y^2$ is $2\cdot 3\cdot y^{(2-1)} = 6y$ .
Differentiate $-\sin(y)$ : Differentiate $-\sin(y)$ with respect to $y$ . The derivative of $\sin(y)$ with respect to $y$ is $\cos(y)$ , so the derivative of $-\sin(y)$ is $-\cos(y)$ .
Combine Derivatives: Combine the derivatives of the two terms to get the derivative of the entire function. The derivative of $3y^2 - \sin(y)$ with respect to $y$ is $6y - \cos(y)$ .