Given y=-csc(3x), find (dy)/(dx). Answer: (dy)/(dx)=

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Given  y=-csc(3x), find  (dy)/(dx). Answer:  (dy)/(dx)=

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Recall definition of cosecant function: Recall the definition of the cosecant function and its derivative. The cosecant function is defined as csc(x) = 1/sin(x), and its derivative with respect to x is given by (d/dx)csc(x) = -csc(x)cot(x). We will use this information to find the derivative of y = -csc(3x) with respect to x.Apply chain rule to differentiate: Apply the chain rule to differentiate y = -csc(3x). The chain rule states that the derivative of a composite function f(g(x)) is f'(g(x))g'(x). In this case, f(x) = -csc(x) and g(x) = 3x. We need to find the derivative of f with respect to g, which is f'(g(x)), and then multiply it by the derivative of g with respect to x, which is g'(x).Differentiate f(g(x)) with respect to g: Differentiate f(g(x)) = -csc(g(x)) with respect to g. Using the derivative of the cosecant function from Step 1, we get f'(g(x)) = -(-csc(g(x))cot(g(x))) = csc(g(x))cot(g(x)).Differentiate g(x) with respect to x: Differentiate g(x) = 3x with respect to x. The derivative of g(x) with respect to x is g'(x) = 3.Combine results using chain rule: Combine the results from Steps 3 and 4 using the chain rule. Multiply f'(g(x)) by g'(x) to get the derivative of y with respect to x. This gives us (dy)/(dx) = csc(3x)cot(3x) * 3.Simplify the derivative: Simplify the expression for the derivative. Since there is a negative sign in the original function y = -csc(3x), we need to include this in our final derivative. The correct derivative is (dy)/(dx) = -3csc(3x)cot(3x).

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

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Given y=−csc⁡(3x) y=-\csc (3 x) y=−csc(3x), find dydx \frac{d y}{d x} dxdy​.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

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