Question

what is the derivative of e^x+log_e(x)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Step-by-step  

Answer:

x+2

x

Explanation:

This can be significantly simplified first using logarithm rules. The first we will use is that log(AB)=log(A)+log(B), so:

y=ln(x2ex)=ln(x2)+ln(ex)

Since ln(x)=loge(x) and ex, are inverse functions, we see that ln(ex)=x. Furthermore, we will also use log(AB)=Blog(A) for ln(x2):

y=2ln(x)+x

Now, to differentiate this, we must know that  

d

dx

ln(x)=

1

x

. Thus:

dy

dx

=

2

x

+1=

x+2

x

explanation: