#### Answer

The derivative is $3t^2+10t-3$.

#### Work Step by Step

Whenever two or more functions are being added or subtracted, the overall derivative would be the sum of the derivatives of every smaller function. The derivative of $t^3$ is $3t^2$, the derivative of $5t^2$ is 10t, the derivative of -3t is -3 and finally the derivative of 8 is 0; hence, the overall derivative is $3t^2+10t-3$.