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

Answer

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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