Calculate the derivative of the given function without using either the product or quotient rule

s(x) = 8 / x^2

Question

Calculate the derivative of the given function without using either the product or quotient rule

s(x) = 8 / x^2

campbell_st · Answer

rewrite the function 

$$s(x) = 8x^{-2}$$

nowapply the normal rule for differentiating

anonymous · Answer

use the power rule. the function really is 8x^-2.

anonymous · Answer

-64x?

campbell_st · Answer

nope... the rule is 

$$f(x) = x^n..... then.... f'(x) = nx^{n - 1}$$

campbell_st · Answer

so its

$$s'(x) = 8 \times -2 x^{-2 -1}$$

just finish it off.

anonymous · Answer

8 ( -1/8x) is this correct so far?

campbell_st · Answer

nope... just look at my last posts..

anonymous · Answer

i did,  i dont know how to calculate when i reach $$8(-2x)^-3$$

campbell_st · Answer

almost you can multiply 8 and -2 to get the coefficient of x

then rewrite the problem in index form.

campbell_st · Answer

opps in non index form

campbell_st · Answer

$$s'(x) = \frac{-16}{x^3}$$

campbell_st · Answer

the power of -3 is only operating on x.... and not -2

anonymous · Answer

so -16x^-3. but im stuck on how to calculate it

anonymous · Answer

oh ok

anonymous · Answer

i got the concept now, thanks for the help

campbell_st · Answer

what do need to calculate, you have the derivative. Do you have a point or x-value to substitute into the derivative?