## anonymous 4 years ago derivative 4^x+6 could you explain in simple terms how to do this in steps, I know its ln, but just stuck in a rut

1. precal

are you trying to take the derivative of 4^x + 6?

2. anonymous

yes

3. lgbasallote

is x + 6 in the exponent?

4. anonymous

no sorry x^4 then +6

5. anonymous

|dw:1328660528124:dw|

6. UnkleRhaukus

${d(x^4+6)\over dx}$ ${d(x^4)\over dx}+{d(6)\over dx}=4x^3+0$

7. anonymous

i mean 4^x + 6 i apologize again

8. anonymous

This is referred to as the power rule..multiply the coefficient by the exponent and then subtract one from the exponent.

9. lgbasallote

oh. okay let y = 4^x + 6 lny = xln4 + ln6 1/y(dy/dx) = ln4 cross multiply.... dy/dx = yln4 substitute... dy/dx = (4^x + 6) ln4 i don't know if that can be simplified further but i think that's simplified already

10. anonymous

|dw:1328660678342:dw|

11. y2o2

2 ln(2)*4^x

12. anonymous

y202 gave the same answer in a different form....both are right.

13. anonymous

ok thank you guys! my text book is terrible over this section, they show the limits only and thats what im not looking for hah,

14. anonymous

so ln(a)*a^x is the format

15. anonymous

yes, I usually write it a^xlna