Differentiate `x^3 - 5 sinx` w.r.t `x`

Answer

To differentiate the function \( y = x^3 - 5 \sin x \) with respect to \( x \), we will follow these steps:

### Step 1: Identify the function
Let \( y = x^3 - 5 \sin x \).

### Step 2: Differentiate each term
We will differentiate the function term by term.

1. Differentiate \( x^3 \):
- Using the power rule, which states that if \( y = x^n \), then \( \frac{dy}{dx} = n x^{n-1} \):
\[ \frac{d}{dx}(x^3) = 3x^{3-1} = 3x^2 \]

2. Differentiate \( -5 \sin x \):
- The constant multiple rule states that if \( y = k f(x) \), then \( \frac{dy}{dx} = k \frac{df}{dx} \). Here, \( k = -5 \) and \( f(x) = \sin x \):
\[ \frac{d}{dx}(-5 \sin x) = -5 \cdot \frac{d}{dx}(\sin x) = -5 \cos x \]

### Step 3: Combine the results
Now, we combine the derivatives from both terms:
\[ \frac{dy}{dx} = 3x^2 - 5 \cos x \]

### Final Answer
Thus, the derivative of the function \( y = x^3 - 5 \sin x \) with respect to \( x \) is:
\[ \frac{dy}{dx} = 3x^2 - 5 \cos x \]

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