Use your knowledge of the derivative to compute the limit given below
lim h→0 ((x+h)^−2.25)−(x^−2.25)/h.

Question

Use your knowledge of the derivative to compute the limit given below
lim  h→0 ((x+h)^−2.25)−(x^−2.25)/h.

parthkohli · Answer

$$\lim_{h \to 0} {(x + h)^{-2.25} - (x^{-2.25}) \over h}$$Notice that this is actually the derivative of nothing, but $x^{-2.25}$. Use the power rule to simplify the rest.

parthkohli · Answer

Why is this the derivative of $x^{-2.25}$? The definition of a derivative says that,$$f'(x) = \lim_{h \to0} {f(x + h) - f(x) \over h}$$So, $f(x) = x^{-2.25}$ after comparing the above definition with your question. And we have to find ${d \over dx}x^{-2.25}$.

parthkohli · Answer

The rest should be very easy for you.

anonymous · Answer

yes i understand now thank you so much!

parthkohli · Answer

You're welcome :)