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Given that 3x-tan y=4, what is (dy)/(dx) in terms of y ?

Given that 3x−tan⁡y=4 3 x-\tan y=4 , what is dydx \frac{d y}{d x} in terms of y y ?

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Full solution

Q. Given that 3x−tan⁡y=4 3 x-\tan y=4 , what is dydx \frac{d y}{d x} in terms of y y ?
  1. Identify Equation: Identify the equation and differentiate both sides with respect to xx.\newlineddx(3x−tan⁡(y))=ddx(4) \frac{d}{dx}(3x - \tan(y)) = \frac{d}{dx}(4)
  2. Apply Derivative: Apply the derivative to each term.\newline3−sec⁡2(y)dydx=0 3 - \sec^2(y) \frac{dy}{dx} = 0
  3. Solve for dy/dx: Solve for dydx\frac{dy}{dx}.\newlinesec⁡2(y)dydx=3 \sec^2(y) \frac{dy}{dx} = 3 \newlinedydx=3sec⁡2(y) \frac{dy}{dx} = \frac{3}{\sec^2(y)}

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