Question

let (f(x)=7sin(x)-2x^{3}). (f(x)=square) worked example: derivatives of (sin(x)) and (cos(x)) related content

Explanation:

Step1: Apply derivative rules

The derivative of $\sin(x)$ is $\cos(x)$ and the derivative of $x^n$ is $nx^{n - 1}$. For $y = 7\sin(x)-2x^{3}$, we use the sum - difference rule of derivatives $\frac{d}{dx}(u - v)=\frac{d}{dx}(u)-\frac{d}{dx}(v)$.

Step2: Differentiate each term

The derivative of $7\sin(x)$ is $7\cos(x)$ (since $\frac{d}{dx}(a\cdot f(x))=a\cdot\frac{d}{dx}(f(x))$ where $a = 7$ and $f(x)=\sin(x)$), and the derivative of $- 2x^{3}$ is $-2\times3x^{2}=-6x^{2}$.

Answer:

$7\cos(x)-6x^{2}$