Given that y=v^(4)+2, find (d)/(dv)(3y^(2)+4cos v) in terms of only v. Answer:

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Given that  y=v^(4)+2, find  (d)/(dv)(3y^(2)+4cos v) in terms of only  v. Answer:

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Given Function: We are given the function y in terms of v: y = v^4 + 2 We need to find the derivative of the expression 3y^2 + 4cos(v) with respect to v. To do this, we will use the chain rule for differentiation, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.Derivative of y: First, let's find the derivative of y with respect to v: y = v^4 + 2 dy/dv = d/dv(v^4) + d/dv(2) dy/dv = 4v^3 + 0 dy/dv = 4v^3Derivative of 3y^2: Now, let's differentiate the expression 3y^2 with respect to y: d/dy(3y^2) = 6yChain Rule Application: Using the chain rule, we can now find the derivative of 3y^2 with respect to v: d/dv(3y^2) = d/dy(3y^2) * dy/dv d/dv(3y^2) = 6y * 4v^3 d/dv(3y^2) = 24yv^3Derivative of 4cos(v): Next, we differentiate 4cos(v) with respect to v: d/dv(4cos(v)) = -4sin(v)Combining Derivatives: Now we can combine the derivatives of both parts of the expression: d/dv(3y^2 + 4cos(v)) = d/dv(3y^2) + d/dv(4cos(v)) d/dv(3y^2 + 4cos(v)) = 24yv^3 - 4sin(v)Substitution and Final Result: Finally, we substitute the expression for y in terms of v into the derivative: d/dv(3y^2 + 4cos(v)) = 24(v^4 + 2)v^3 - 4sin(v) d/dv(3y^2 + 4cos(v)) = 24v^7 + 48v^3 - 4sin(v)

Given that $y=v^{4}+2$ , find $\frac{d}{d v}\left(3 y^{2}+4 \cos v\right)$ in terms of only $v$ . $\newline$ Answer:

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Given that y=v4+2 y=v^{4}+2 y=v4+2, find ddv(3y2+4cos⁡v) \frac{d}{d v}\left(3 y^{2}+4 \cos v\right) dvd​(3y2+4cosv) in terms of only v v v.\newlineAnswer:

Given that $y=v^{4}+2$ , find $\frac{d}{d v}\left(3 y^{2}+4 \cos v\right)$ in terms of only $v$ . $\newline$ Answer: