How do you use the definition of a derivative to find the derivative of f(x)=8x?

Dec 28, 2016

definition of derivative

$\frac{\mathrm{dy}}{\mathrm{dx}} = L i {m}_{h \rightarrow 0} \frac{f \left(x + h\right) - f \left(x\right)}{h}$

Explanation:

for $\text{ } f \left(x\right) = 8 x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = L i {m}_{h \rightarrow 0} \frac{\left(8 \left(x + h\right) - 8 x\right)}{h}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = L i {m}_{h \rightarrow 0} \frac{\left(\cancel{8 x} + 8 h \cancel{- 8 x}\right)}{h}$

(dy)/(dx)=Lim_(hrarr0)(8cancel(h))/cancel(h

$\frac{\mathrm{dy}}{\mathrm{dx}} = L i {m}_{h \rightarrow 0} \left(8\right) = 8$