Find the derivative of given function w.r.t. corresponding independent variable
`y=5sin x`

Options

A. `5 cos x`
B. 5
C. `sin x`
D. `5+cos x`

Answer

To find the derivative of the function \( y = 5 \sin x \) with respect to the independent variable \( x \), we will follow these steps:

### Step 1: Identify the function
We have the function:
\[ y = 5 \sin x \]

### Step 2: Apply the derivative rule
To differentiate \( y \) with respect to \( x \), we will use the constant multiple rule and the derivative of the sine function. The derivative of \( \sin x \) is \( \cos x \).

### Step 3: Differentiate the function
Using the rules mentioned:
\[ \frac{dy}{dx} = 5 \cdot \frac{d}{dx}(\sin x) \]
Since the derivative of \( \sin x \) is \( \cos x \), we have:
\[ \frac{dy}{dx} = 5 \cdot \cos x \]

### Step 4: Write the final answer
Thus, the derivative of the function \( y = 5 \sin x \) with respect to \( x \) is:
\[ \frac{dy}{dx} = 5 \cos x \]

---