Given y=3cot^(3)(x), find (dy)/(dx). Answer: (dy)/(dx)=

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Given  y=3cot^(3)(x), find  (dy)/(dx). Answer:  (dy)/(dx)=

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Identify Function: Identify the function to differentiate. We are given the function y = 3cot^(3)(x), which means y is equal to three times the cube of the cotangent of x.Apply Chain Rule: Apply the chain rule for differentiation. The chain rule 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. In this case, the outer function is f(u) = 3u^3 and the inner function is u(x) = cot(x). We need to find the derivative of both functions.Differentiate Outer Function: Differentiate the outer function f(u) = 3u^3 with respect to u. The derivative of f(u) with respect to u is f'(u) = 3 * 3u^(3-1) = 9u^2.Differentiate Inner Function: Differentiate the inner function u(x) = cot(x) with respect to x. The derivative of cot(x) with respect to x is -csc^2(x), where csc(x) is the cosecant of x.Apply Chain Rule with Derivatives: Apply the chain rule using the derivatives from steps 3 and 4. (dy)/(dx) = f'(u) * (du)/(dx) = 9u^2 * (-csc^2(x)) = 9cot^2(x) * (-csc^2(x)).Substitute Back to x: Substitute u back with cot(x) to get the derivative in terms of x. (dy)/(dx) = 9cot^2(x) * (-csc^2(x)) = -9cot^2(x)csc^2(x).Check for Errors: Check for any mathematical errors in the differentiation process. No mathematical errors were made in the differentiation process.

Given $y=3 \cot ^{3}(x)$ , find $\frac{d y}{d x}$ . $\newline$ Answer: $\frac{d y}{d x}=$

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Given y=3cot⁡3(x) y=3 \cot ^{3}(x) y=3cot3(x), find dydx \frac{d y}{d x} dxdy​.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given $y=3 \cot ^{3}(x)$ , find $\frac{d y}{d x}$ . $\newline$ Answer: $\frac{d y}{d x}=$