Given that u=w^(3)-4, find (d)/(dw)(4u^(2)+5cos w) in terms of only w. Answer:

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Given that  u=w^(3)-4, find  (d)/(dw)(4u^(2)+5cos w) in terms of only  w. Answer:

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Given function u: We are given the function u in terms of w: u = w^3 - 4 We need to find the derivative of the expression 4u^2 + 5cos(w) with respect to w. 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 u: First, let's find the derivative of u with respect to w: du/dw = d(w^3 - 4)/dw Using the power rule, we get: du/dw = 3w^2Derivative of 4u^2: Now, let's differentiate the expression 4u^2 with respect to u: d(4u^2)/du = 8uChain rule application: Next, we apply the chain rule to find the derivative of 4u^2 with respect to w: d(4u^2)/dw = d(4u^2)/du * du/dw Substitute the derivatives we found: d(4u^2)/dw = 8u * 3w^2Derivative of 5cos(w): Now, let's differentiate 5cos(w) with respect to w: d(5cos(w))/dw = -5sin(w)Combining derivatives: Combine the derivatives of 4u^2 and 5cos(w) to find the total derivative with respect to w: d/dw(4u^2 + 5cos(w)) = d(4u^2)/dw + d(5cos(w))/dw Substitute the derivatives we found: d/dw(4u^2 + 5cos(w)) = 8u * 3w^2 - 5sin(w)Expressing u in terms of w: Now, we need to express u in terms of w using the given u = w^3 - 4: d/dw(4u^2 + 5cos(w)) = 8(w^3 - 4) * 3w^2 - 5sin(w)Simplifying the expression: Simplify the expression: d/dw(4u^2 + 5cos(w)) = 24w^2(w^3 - 4) - 5sin(w)

Given that $u=w^{3}-4$ , find $\frac{d}{d w}\left(4 u^{2}+5 \cos w\right)$ in terms of only $w$ . $\newline$ Answer:

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Given that u=w3−4 u=w^{3}-4 u=w3−4, find ddw(4u2+5cos⁡w) \frac{d}{d w}\left(4 u^{2}+5 \cos w\right) dwd​(4u2+5cosw) in terms of only w w w.\newlineAnswer:

Given that $u=w^{3}-4$ , find $\frac{d}{d w}\left(4 u^{2}+5 \cos w\right)$ in terms of only $w$ . $\newline$ Answer: