Given y=2cot^(3)(x), find (dy)/(dx). Answer: (dy)/(dx)=

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Given  y=2cot^(3)(x), find  (dy)/(dx). Answer:  (dy)/(dx)=

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Identify Function: Identify the function to differentiate. The function given is y = 2cot^(3)(x), which means y = 2[cot(x)]^3.Apply Chain Rule: Recognize that to differentiate y with respect to x, we need to apply the chain rule because we have a function raised to a power. The chain rule states that the derivative of a composite function f(g(x)) is f'(g(x))g'(x).Differentiate Outer Function: Differentiate the outer function first, keeping the inner function the same. The outer function is u^3 where u = cot(x), and its derivative with respect to u is 3u^2. So, the derivative of the outer function with respect to cot(x) is 3[cot(x)]^2.Differentiate Inner Function: Now, differentiate the inner function, which is cot(x). The derivative of cot(x) with respect to x is -csc^2(x), where csc(x) is the cosecant function.Apply Chain Rule Again: Apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function. This gives us the derivative of y with respect to x: (dy)/(dx) = 3[cot(x)]^2 * (-csc^2(x)).Multiply by Constant Factor: Finally, multiply the result by the constant factor from the original function, which is 2. This gives us (dy)/(dx) = 2 * 3[cot(x)]^2 * (-csc^2(x)).Simplify and Final Answer: Simplify the expression by combining constants and writing the final answer. The constants 2 and 3 can be multiplied together to give 6, and the negative sign remains. So, the final answer is (dy)/(dx) = -6[cot(x)]^2 * csc^2(x).

Given $y=2 \cot ^{3}(x)$ , find $\frac{d y}{d x}$ . $\newline$ Answer: $\frac{d y}{d x}=$

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Given y=2cot⁡3(x) y=2 \cot ^{3}(x) y=2cot3(x), find dydx \frac{d y}{d x} dxdy​.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given $y=2 \cot ^{3}(x)$ , find $\frac{d y}{d x}$ . $\newline$ Answer: $\frac{d y}{d x}=$