Derivatives:
y=x^1/8(6^x)

Question

Derivatives:
y=x^1/8(6^x)

anonymous · Answer

Product rule! f = x^(1/8) and g = 6^x. 

Now find f' and g' and plug it into the formula: f'g + g'f

anonymous · Answer

@BluFoot  ok... I got f' = (x/8)^-7/8    if that makes sense...
but how exactly do you work out the g'?

anonymous · Answer

Use this rule:

derivative of a^x = a^x * ln(a)
where a is any number

anonymous · Answer

@BluFoot  I got:
g' = 6^x * In ^ 6
so my final answer is:
f'g + g'f =  $$x/8^(- 7/8) * 6^x + 6^x * In 6 * x^ (1/8)$$

anonymous · Answer

Perfect, very good! :)

anonymous · Answer

@BluFoot thank you so much!!!!! Just did another example and got the correct answer. I think i've grasped that concept now. :)

anonymous · Answer

Great! You're very welcome! It's much easier when you make a little table or something where you write f = this, g= that, f' = derivative of this, g'= derivative of that. Then you just combine the 4 terms and you have your answer :)

anonymous · Answer

I'll be sure to keep that in mind when my test comes up. 
*If only my lecturer made things this simplified...life would be so much better.*
Thank you once again. :)