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Find dy/dx if y-7x=sinx...

Find `dy/dx if y-7x=sinx`

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To find \(\frac{dy}{dx}\) for the equation \(y - 7x = \sin x\), we will follow these steps: ### Step 1: Write the given equation We start with the equation: \[ y - 7x = \sin x \] ### Step 2: Differentiate both sides with respect to \(x\) We will differentiate both sides of the equation with respect to \(x\): \[ \frac{d}{dx}(y - 7x) = \frac{d}{dx}(\sin x) \] ### Step 3: Apply differentiation rules Using the rules of differentiation, we differentiate each term: - The derivative of \(y\) with respect to \(x\) is \(\frac{dy}{dx}\). - The derivative of \(7x\) is \(7\) (since the derivative of \(x\) is \(1\)). - The derivative of \(\sin x\) is \(\cos x\). So, we have: \[ \frac{dy}{dx} - 7 = \cos x \] ### Step 4: Solve for \(\frac{dy}{dx}\) Now, we will isolate \(\frac{dy}{dx}\): \[ \frac{dy}{dx} = \cos x + 7 \] ### Final Answer Thus, the value of \(\frac{dy}{dx}\) is: \[ \frac{dy}{dx} = \cos x + 7 \] ---
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