Given that v=2y^(4)-5, find (d)/(dy)(4v^(2)-cos y) in terms of only y. Answer:

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Given that  v=2y^(4)-5, find  (d)/(dy)(4v^(2)-cos y) in terms of only  y. Answer:

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Express in terms of y: First, we need to express 4v^2 in terms of y using the given expression for v. v = 2y^4 - 5 v^2 = (2y^4 - 5)^2 4v^2 = 4(2y^4 - 5)^2Find derivative of 4v^2: Now, we will find the derivative of 4v^2 with respect to y. Using the chain rule, the derivative of 4v^2 with respect to y is 2 * 4v * dv/dy. Since v = 2y^4 - 5, dv/dy = d/dy(2y^4 - 5) = 8y^3. Therefore, the derivative of 4v^2 with respect to y is 2 * 4 * (2y^4 - 5) * 8y^3.Simplify derivative expression: Next, we simplify the expression for the derivative of 4v^2 with respect to y. 2 * 4 * (2y^4 - 5) * 8y^3 = 64y^3 * (2y^4 - 5)Find derivative of -cos(y): Now, we find the derivative of -cos(y) with respect to y. The derivative of -cos(y) with respect to y is sin(y).Combine derivatives: Finally, we combine the derivatives of 4v^2 and -cos(y) to find the derivative of the entire expression with respect to y. (d/dy)(4v^2 - cos(y)) = 64y^3 * (2y^4 - 5) + sin(y)Express final answer: We express the final answer in terms of y. (d/dy)(4v^2 - cos(y)) = 128y^7 - 320y^3 + sin(y)

Given that $v=2 y^{4}-5$ , find $\frac{d}{d y}\left(4 v^{2}-\cos y\right)$ in terms of only $y$ . $\newline$ Answer:

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Given that v=2y4−5 v=2 y^{4}-5 v=2y4−5, find ddy(4v2−cos⁡y) \frac{d}{d y}\left(4 v^{2}-\cos y\right) dyd​(4v2−cosy) in terms of only y y y.\newlineAnswer:

Given that $v=2 y^{4}-5$ , find $\frac{d}{d y}\left(4 v^{2}-\cos y\right)$ in terms of only $y$ . $\newline$ Answer: