Question

differentiate 2^x^3

Answer 1

\[(2x^3)'=3\cdot2x^{3-1}=6x^2\]

Answer 2

its 2 to the power x to the power 3

Answer 3

put y=(2^x^3)...
use logarithms on both sides then differentiate.
You need to find dy/dx :)
Hope this helps.

Answer 4

:(

Answer 5

@yashdhanuka - did you not understand ??

Answer 6

no

Answer 7

ln(y)=(x^3) (ln(2))

did u understand this ???

Answer 8

yes

Answer 9

@yashdhanuka we use logarithmic function to take powers in multiplication so that it is easy to solve :)

Answer 10

d(ln(y))/dx = (1/y)*(dy/dx)
did u understand this ??

Answer 11

yes

Answer 12

thanks a lot @xavier123 :)

Answer 13

i got the the answer

Answer 14

\[\LARGE y = 2^{x^{3}}\] take natural logs of both sides
\[\LARGE \ln y = \ln 2^{x^{3}}\]
\[\Large \ln y = x^3 \ln 2\]
now either differentiate implicitly, or put both sides to the power of e:

\[\LARGE y = e ^ {x^3 \ln 2}\]
Now differentiate. The derivative of \[\Large e^{f(x)}\] is \[\Large f'(x) e ^ {f(x)}\]

Answer 15

so, differentiate both the sides of the previous equation,
=> dy/dx=(y)* d(x^3)/dx and evaluate.

Answer 16

thanks a ton :D

Answer 17

Just more generally, @agent0smith
\[\huge \frac{d}{dx}a^{f(x)}=\ln(a)f'(x)a^{f(x)}\]

Answer 18

thanks a lot

Answer 19

Only if a is a constant, ok?

Answer 20

Sorry, XD. I missunderstand the function XD