Find (d)/(dw)(w^(2)+5cos w) Answer:

Given function: We are given the function f(w) = w^2 + 5cos(w) and we need to find its derivative with respect to w, which is denoted as (d/dw)(w^2 + 5cos(w)).Sum rule application: To find the derivative of the function, we will apply the sum rule of differentiation, which states that the derivative of a sum of functions is the sum of their derivatives. We will also use the power rule for the w^2 term and the chain rule for the 5cos(w) term.Derivative of w^2: First, let's find the derivative of the first term, w^2. Using the power rule, which states that the derivative of w^n is n*w^(n-1), we get: (d/dw)(w^2) = 2wDerivative of 5cos(w): Now, let's find the derivative of the second term, 5cos(w). The derivative of cos(w) with respect to w is -sin(w), and since we have a constant multiple of 5, we use the constant multiple rule to get: (d/dw)(5cos(w)) = 5 * (d/dw)(cos(w)) = 5 * (-sin(w)) = -5sin(w)Combining derivatives: Combining the derivatives of both terms, we get the derivative of the entire function: (d/dw)(w^2 + 5cos(w)) = (d/dw)(w^2) + (d/dw)(5cos(w)) = 2w - 5sin(w)

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Algebra 2

Evaluate expression when two complex numbers are given

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Q. Find

\frac{d}{d w}\left(w^{2}+5 \cos w\right)

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Answer:

Given function: We are given the function $f(w) = w^2 + 5\cos(w)$ and we need to find its derivative with respect to $w$ , which is denoted as $\frac{d}{dw}(w^2 + 5\cos(w))$ .
Sum rule application: To find the derivative of the function, we will apply the sum rule of differentiation, which states that the derivative of a sum of functions is the sum of their derivatives. We will also use the power rule for the $w^2$ term and the chain rule for the $5\cos(w)$ term.
Derivative of $w^2$ : First, let's find the derivative of the first term, $w^2$ . Using the power rule, which states that the derivative of $w^n$ is $n*w^{(n-1)}$ , we get: $\newline$ $(d/dw)(w^2) = 2w$
Derivative of $5\cos(w)$ : Now, let's find the derivative of the second term, $5\cos(w)$ . The derivative of $\cos(w)$ with respect to $w$ is $-\sin(w)$ , and since we have a constant multiple of $5$ , we use the constant multiple rule to get: $\newline$ $(\frac{d}{dw})(5\cos(w)) = 5 \times (\frac{d}{dw})(\cos(w)) = 5 \times (-\sin(w)) = -5\sin(w)$
Combining derivatives: Combining the derivatives of both terms, we get the derivative of the entire function: $\newline$ $(\frac{d}{dw})(w^2 + 5\cos(w)) = (\frac{d}{dw})(w^2) + (\frac{d}{dw})(5\cos(w)) = 2w - 5\sin(w)$