Use the following limit definition to determine the slope of the line tangent to the graph of $f$ at $P$, where $f\left(x\right)=\frac{19}{x^3}$ and $P(-1,-19)$:

$m_{\text{tan}}=\underset{x\to a}{\lim }\frac{f\left(x\right)-f\left(a\right)}{x-a}$

Determine the equation of the line perpendicular to the tangent line of the curve $y=2x+5$ at the point $Q(2,9)$.

Let $f^{}\left(x\right)=h\left(g\left(x\right)\right)$. Calculate $f^{\prime }\left(4\right)$ using the following table:

Determine the derivative of the function $f\left(x\right)=$ $4x^4$ using the definition:

$f^{\prime}\left(x\right)={\displaystyle\lim_{h\to0}}\text{ }\frac{f\left(x+h\right)-f\left(x\right)}{h}$

The graph of a function $y=j\left(x\right)$ is given below. Use this graph to draw the graph of its derivative $j^{\prime }\left(x\right)$.

Given the graph of a function $f\left(x\right)$, draw the graph of $f^{\prime }\left(x\right)$.

Determine the values of $x\in (-3,3)$ at which $f$ is not differentiable using the following graph: