can someone show me how to use extended power rule within the quotient rule for derivative?

http://webwork.math.ttu.edu/wwtmp/equations/10/ab7506a44aafa9272098cb86d31c771.png

Question

can someone show me how to use extended power rule within the quotient rule for derivative?

http://webwork.math.ttu.edu/wwtmp/equations/10/ab7506a44aafa9272098cb86d31c771.png

amistre64 · Answer

you want derivative of that?

anonymous · Answer

yes using extended power rule

amistre64 · Answer

ive never heard of an extended power rule

anonymous · Answer

that makes two of us haha

amistre64 · Answer

h(x) = tan(3x) * (x)^(-2)

anonymous · Answer

the question calls for extended power rule inside quotient rule. I have an example in my book but it docent really make sense

amistre64 · Answer

lets see it if you can

anonymous · Answer

if i can derive what you just typed?

amistre64 · Answer

recall that a negative exponent is just a fraction in disguise

amistre64 · Answer

no, the example ...

anonymous · Answer

$$p(x)=\tan7x/(1-4x)^5$$

anonymous · Answer

and the answer is$$(7(1-4x)\sec^2(7x)+20\tan7x)/(1-4x)^6$$

amistre64 · Answer

thats the answer regardless of any extended power rule .. 

the parts inbetween would shed some light on this enigma :)

amistre64 · Answer

its just the chain rule ...

anonymous · Answer

how do i know what to sub for u?

amistre64 · Answer

you aint got to sub for anything :/

anonymous · Answer

wait i think i get it. thx

amistre64 · Answer

you were apparently taught that derivatives act on a variable; as opposed to a function ...

amistre64 · Answer

derivaite of y(x) = y'(x) * x' , but x' wrt x = 1

amistre64 · Answer

y = 2x -> y' = 2

  really should be taught as

y = 2x  ->  y' = 2x * x'

and as long as the derivative is with respect to x then x'=1

amistre64 · Answer

the chain rule always pops out a derivative but they simply dont teach that at first ....

amistre64 · Answer

if i asked you to take the derivative of:

y = 5x^2 + 6

what would you assume?