Given that u=3v^(4)+1, find (d)/(dv)(u^(2)-cos v) in terms of only v. Answer:

Question

Given that  u=3v^(4)+1, find  (d)/(dv)(u^(2)-cos v) in terms of only  v. Answer:

Bytelearn · Accepted Answer

Express in terms of v: First, we need to express u^2 - cos(v) in terms of v using the given expression for u. u = 3v^4 + 1 u^2 = (3v^4 + 1)^2 Now, we have u^2 - cos(v) = (3v^4 + 1)^2 - cos(v)Find derivative of u^2: Next, we will find the derivative of u^2 with respect to v. To do this, we will use the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. Let's denote f(v) = u^2 and g(v) = 3v^4 + 1. Then f(g(v)) = (3v^4 + 1)^2. Using the chain rule, we get: (d)/(dv)(u^2) = (d)/(du)(u^2) * (d)/(dv)(u) = 2u * (d)/(dv)(3v^4 + 1) = 2u * (12v^3) = 24v^3 * uFind derivative of -cos(v): Now, we need to find the derivative of -cos(v) with respect to v. (d)/(dv)(-cos(v)) = sin(v)Combine derivatives: We can now combine the derivatives to find the derivative of the entire expression u^2 - cos(v) with respect to v. (d)/(dv)(u^2 - cos(v)) = (d)/(dv)(u^2) + (d)/(dv)(-cos(v)) = 24v^3 * u + sin(v)Substitute back into expression: Finally, we substitute u back into the expression in terms of v. u = 3v^4 + 1 (d)/(dv)(u^2 - cos(v)) = 24v^3 * (3v^4 + 1) + sin(v) = 72v^7 + 24v^3 + sin(v)

Given that $u=3 v^{4}+1$ , find $\frac{d}{d v}\left(u^{2}-\cos v\right)$ in terms of only $v$ . $\newline$ Answer:

Full solution

More problems from Find the roots of factored polynomials

Related topics

Given that u=3v4+1 u=3 v^{4}+1 u=3v4+1, find ddv(u2−cos⁡v) \frac{d}{d v}\left(u^{2}-\cos v\right) dvd​(u2−cosv) in terms of only v v v.\newlineAnswer:

Given that $u=3 v^{4}+1$ , find $\frac{d}{d v}\left(u^{2}-\cos v\right)$ in terms of only $v$ . $\newline$ Answer: