Given y=-2sin(2x), find (dy)/(dx). Answer: (dy)/(dx)=

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Given  y=-2sin(2x), find  (dy)/(dx). Answer:  (dy)/(dx)=

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Identify Function: Identify the function to differentiate. We are given the function y = -2sin(2x) and we need to find its derivative with respect to 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 -2sin(u) where u = 2x, and the inner function is 2x.Differentiate Outer Function: Differentiate the outer function with respect to the inner function u. The derivative of -2sin(u) with respect to u is -2cos(u), because the derivative of sin(u) with respect to u is cos(u) and we have a constant multiplier of -2.Differentiate Inner Function: Differentiate the inner function with respect to x. The derivative of 2x with respect to x is 2, because the derivative of x with respect to x is 1 and we have a constant multiplier of 2.Apply Chain Rule: Apply the chain rule by multiplying the derivatives from Step 3 and Step 4. (dy)/(dx) = (-2cos(u)) * (2) where u = 2x.Substitute Back: Substitute u back into the equation to express the derivative in terms of x. (dy)/(dx) = (-2cos(2x)) * (2) = -4cos(2x).

Given $y=-2 \sin (2 x)$ , find $\frac{d y}{d x}$ . $\newline$ Answer: $\frac{d y}{d x}=$

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Given y=−2sin⁡(2x) y=-2 \sin (2 x) y=−2sin(2x), find dydx \frac{d y}{d x} dxdy​.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given $y=-2 \sin (2 x)$ , find $\frac{d y}{d x}$ . $\newline$ Answer: $\frac{d y}{d x}=$