Home > CALC > Chapter Ch3 > Lesson 3.4.3 > Problem3-176

3-176.

These are both Hana's definition of the derivative. Instead of algrabraically finding these limits (as you did in 3-175), you could deconstruct her definition and apply the power rule.

Hana's definition of the derivative:

$f'(x) =\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

What if f(x)? f(x) = x5
What if f '(x)? f '(x) = 5x4

$=\lim_{h\rightarrow 0}\frac{(x+h)^5-x^5}{h}$

Hana's definition of the derivative:

$f'(x) =\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

What if f(x)? f(x) = ___________
What if f '(x)? f '(x) = ___________

$=\lim_{h\rightarrow 0}\frac{2\sqrt{x+h}-2\sqrt{x}}{h}$