Yasemin tried to find the derivative of $x^{6} \cdot \cos (x)$. Here is her work:

Step 1: This is the product of $\cos (x)$ and $x^{6}$. So, we should use the product rule.
Step 2:

$\frac{d}{d x}[x^{6} \cdot \cos (x)]=\frac{d}{d x}[\cos (x)] \cdot x^{6}+\cos (x) \cdot \frac{d}{d x}[x^{6}]$

Step 3: Finding the derivatives of the factors:

$\frac{d}{d x}[\cos (x)] =-\sin (x)$

$\frac{d}{d x}[x^{6}] =6 x^{5}$

Step 4: Putting it all together:

$\frac{d}{d x}[x^{6} \cdot \cos (x)]=\frac{d}{d x}[\cos (x)] \cdot x^{6}+\cos (x) \cdot \frac{d}{d x}[x^{6}]=-\sin ({x}) \cdot x^{6}+6 x^{5} \cos (x)$

Is Yasemin’s work correct? If not, what’s her mistake?