Example Derivative Calculation

$y=3x^5-3x^4+7x^3-5x^2+x-8$ 

Step 1: Multiply both side by d/dx

$\frac{dy}{dx}=\frac{d}{dx}(3x^5-3x^4+7x^3-5x^2+x-8)$

$$\begin{gathered} \text{ \\ dydx=ddx3x5-ddx3x4+ddx7x3-ddx5x2+ddxx-ddx8 \\ } \end{gathered}$$

$\mathrm{Remember}:$

$$\begin{gathered} \text{ \\ (1) ddx(cxn)=cnxn-1} \end{gathered}$$

$$\begin{gathered} \text{ \\ (2) ddx(x) = 1} \end{gathered}$$

$$\begin{gathered} \text{ \\ (3) ddx(c) = 0 \\ } \end{gathered}$$

$$\begin{gathered} \mathrm{Final} \mathrm{Answer}: \\ \frac{dy}{dx}=15x^4-12x^3+21x^2-10x+1 \end{gathered}$$