Find (d)/(dw)(2w^(2)+4cos w) Answer:

Identify function: Identify the function to differentiate. We are given the function f(w) = 2w^2 + 4cos(w), and we need to find its derivative with respect to w.Apply power rule: Apply the power rule to the first term. The power rule states that the derivative of w^n with respect to w is n*w^(n-1). Applying this to the first term 2w^2, we get: (d/dw)(2w^2) = 2 * 2w^(2-1) = 4wApply cosine derivative rule: Apply the derivative rule for the cosine function to the second term. The derivative of cos(w) with respect to w is -sin(w). Applying this to the second term 4cos(w), we get: (d/dw)(4cos(w)) = 4 * (-sin(w)) = -4sin(w)Combine derivatives: Combine the derivatives of both terms. Now we combine the derivatives from Step 2 and Step 3 to find the derivative of the entire function: (d/dw)(2w^2 + 4cos(w)) = 4w - 4sin(w)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find $\frac{d}{d w}\left(2 w^{2}+4 \cos w\right)$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find

\frac{d}{d w}\left(2 w^{2}+4 \cos w\right)

\newline

Answer:

Identify function: Identify the function to differentiate. $\newline$ We are given the function $f(w) = 2w^2 + 4\cos(w)$ , and we need to find its derivative with respect to $w$ .
Apply power rule: Apply the power rule to the first term. $\newline$ The power rule states that the derivative of $w^n$ with respect to $w$ is $n\cdot w^{n-1}$ . Applying this to the first term $2w^2$ , we get: $\newline$ $\frac{d}{dw}(2w^2) = 2 \cdot 2w^{2-1} = 4w$
Apply cosine derivative rule: Apply the derivative rule for the cosine function to the second term. $\newline$ The derivative of $\cos(w)$ with respect to $w$ is $-\sin(w)$ . Applying this to the second term $4\cos(w)$ , we get: $\newline$ $(\frac{d}{dw})(4\cos(w)) = 4 \times (-\sin(w)) = -4\sin(w)$
Combine derivatives: Combine the derivatives of both terms. $\newline$ Now we combine the derivatives from Step $2$ and Step $3$ to find the derivative of the entire function: $\newline$ $(\frac{d}{dw})(2w^2 + 4\cos(w)) = 4w - 4\sin(w)$