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

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

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Identify Function and Rules: Identify the function to differentiate and the rules that will be applied. The function is y = 3cot(2x), and we will use the chain rule and the derivative of cotangent.Recall Cotangent Derivative: Recall the derivative of cotangent. The derivative of cot(x) with respect to x is -csc^2(x), where csc is the cosecant function.Apply Chain Rule: Apply the chain rule. The chain rule states that the derivative of a composite function f(g(x)) is f'(g(x))g'(x). Here, f(x) = 3cot(x) and g(x) = 2x. We need to find the derivative of f with respect to g and then multiply by the derivative of g with respect to x.Differentiate Composite Function: Differentiate f(g(x)) = 3cot(g(x)) with respect to g. The derivative is -3csc^2(g(x)) because the derivative of cotangent is -csc^2(x), and we multiply by the constant 3.Differentiate Linear Function: Differentiate g(x) = 2x with respect to x. The derivative is 2 because the derivative of x with respect to x is 1, and we multiply by the constant 2.Combine Derivatives: Combine the derivatives using the chain rule. Multiply the derivative of f with respect to g by the derivative of g with respect to x to get the derivative of y with respect to x. This gives us (dy)/(dx) = -3csc^2(2x) * 2.Simplify Final Result: Simplify the expression. Multiply -3 by 2 to get -6. The final derivative is (dy)/(dx) = -6csc^2(2x).

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

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

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