On differentiating y = 3x we get the result as 3x(log3). How do we get log3 in there? Please explain

Inferno

On differentiating y = 3^x we get the result as 3^x(log3). How do we get log3 in there? Please explain and if possible give one more example.

vijay kharya

either write the infinite series and put x---->0 or use the formula lim x------>( a^x-1)/x = ln a after taking a^x common ( in this case a=3)

HIMANSHU JAIN

it's easy to analyze.

Whenever, you have variables in exponent, simply take log to ease your headache.

so, taking log:

log y = x*log3.

now, diff

(1/y) dy/dx = log3.

now, is it clear from where log3 came into picture :)