Given that x=u^(2)+2, find (d)/(du)(2x^(3)-3sin u) in terms of only u. Answer:

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Given that  x=u^(2)+2, find  (d)/(du)(2x^(3)-3sin u) in terms of only  u. Answer:

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Express x in terms of u: First, we need to express x in terms of u, which is already given as x = u^2 + 2. We will use this to find the derivative of x with respect to u.Calculate derivative of x: Calculate the derivative of x with respect to u, which is dx/du. dx/du = d(u^2 + 2)/du dx/du = 2u + 0 dx/du = 2uApply chain rule: Now, we need to find the derivative of the expression 2x^3 - 3sin u with respect to x and then with respect to u. We will use the chain rule for this, which states that d/dx(f(g(x))) = f'(g(x)) * g'(x).Find derivative of 2x^3: First, find the derivative of 2x^3 with respect to x. d(2x^3)/dx = 6x^2Find derivative of -3sin u: Next, find the derivative of -3sin u with respect to u. d(-3sin u)/du = -3cos uApply chain rule to find derivative of 2x^3: Now, apply the chain rule to find the derivative of 2x^3 with respect to u. d(2x^3)/du = d(2x^3)/dx * dx/du d(2x^3)/du = 6x^2 * 2uSubstitute x into derivative: Substitute x = u^2 + 2 into the derivative of 2x^3 with respect to u. d(2x^3)/du = 6(u^2 + 2)^2 * 2uSimplify the expression: Simplify the expression. d(2x^3)/du = 12u(u^2 + 2)^2Combine derivatives: Combine the derivatives of 2x^3 and -3sin u with respect to u to get the final derivative of the expression 2x^3 - 3sin u with respect to u. d(2x^3 - 3sin u)/du = 12u(u^2 + 2)^2 - 3cos u

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

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Given that x=u2+2 x=u^{2}+2 x=u2+2, find ddu(2x3−3sin⁡u) \frac{d}{d u}\left(2 x^{3}-3 \sin u\right) dud​(2x3−3sinu) in terms of only u u u.\newlineAnswer:

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