Business Calculus
It can be concluded that the derivative of f(x)=∣2x∣f\left(x\right)=\left|2x\right|f(x)=∣2x∣ is a vertical compression of y=∣2x∣xy=\frac{\left|2x\right|}{x} by a factor of 22.
It can be concluded that the derivative of f(x)=∣2x∣f\left(x\right)=\left|2x\right|f(x)=∣2x∣ is a vertical stretch of y=∣2x∣xy=\frac{\left|2x\right|}{x}y=x∣2x∣ by a factor of 222.
It can be concluded that the derivative of y=∣2x∣xy=\frac{\left|2x\right|}{x} is the same as the derivative of f(x)=∣2x∣f\left(x\right)=\left|2x\right|.
It can be concluded that the derivative of f(x)=∣2x∣f\left(x\right)=\left|2x\right|f(x)=∣2x∣ is f′(x)=∣2x∣xf^{\prime}\left(x\right)=\frac{\left|2x\right|}{x}f′(x)=x∣2x∣.