Determine the derivative $\frac{dz}{dt}$ and$\left. \frac{dz}{dt} \right|_{t=3}$ for the function $z=\frac{t+2}{t+3}$.

Evaluate the following derivative using the graph given below.

$\frac{\text{d}}{\text{dx}}{\left(xg\left(x\right)\right)}_{x=2}$

Determine the derivative of $f\left(x\right)=\frac{2x^2-3x}{x}$ using the quotient rule.

Determine the slope of the tangent line at the point $(2,\frac{1}{6})$ for the function $p\left(x\right)=\frac{x}{2x+8}$.

Determine the derivative of $h\left(x\right)=\frac{x^{\frac{7}{4}}}{x^{\frac{7}{4}}+5}$.

Find the derivative of the function $y=e^x\cos x$.

For the given four differentiable functions $\left(p,q,r,s\right)$ of $y,$ what is the derivative of their product $pqrs$?