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

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

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Identify Function and Rules: Identify the function that needs to be differentiated and the rules that will be applied. The function is y = 3sec(2x), and we will use the chain rule for differentiation, which 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.Differentiate Outer Function: Differentiate the outer function while keeping the inner function unchanged. The outer function is 3sec(u), where u = 2x. The derivative of sec(u) with respect to u is sec(u)tan(u), so the derivative of 3sec(u) with respect to u is 3sec(u)tan(u).Differentiate Inner Function: Differentiate the inner function. The inner function is u = 2x, and its derivative with respect to x is du/dx = 2.Apply Chain Rule: Apply the chain rule by multiplying the derivatives of the outer and inner functions. The derivative of y with respect to x is (dy/du) * (du/dx) = 3sec(u)tan(u) * 2.Substitute Inner Function: Substitute the inner function back into the derivative to get the final answer. Replace u with 2x to get (dy/dx) = 3sec(2x)tan(2x) * 2.Simplify Final Derivative: Simplify the expression to get the final derivative. The final derivative is (dy/dx) = 6sec(2x)tan(2x).

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

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

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