- #1
apples
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1.
I was trying to understand the proof of
(d/dx) b^x = (ln b)*(b^x)
it says:
b= e^(ln b)
so, b^x= e^((ln b)*x))
So now we use the chain rule:
(d/dx) b^x = (d/dx) e^((ln b)*x))
I understand everything so far, but not the next step.
It says then that
(d/dx) e^((ln b)*x))= (ln b)*e^(ln b)*x)
how did they get this, i am confused about the bold part. I am forgetting something about taking the derivative of the natural number 'e'?
I know that d/dx e^x = x
so how does the ln b come behind e^x above?
what does (d/dx) e^f(x) equal to?
is (d/dx) e^f(x) = f '(x)* e^f(x) ?
if so then
1 + ln b
should come behind that because
d/dx (ln b)*x is equal to 1 + ln b
Please help me
thank you
I was trying to understand the proof of
(d/dx) b^x = (ln b)*(b^x)
it says:
b= e^(ln b)
so, b^x= e^((ln b)*x))
So now we use the chain rule:
(d/dx) b^x = (d/dx) e^((ln b)*x))
I understand everything so far, but not the next step.
It says then that
(d/dx) e^((ln b)*x))= (ln b)*e^(ln b)*x)
how did they get this, i am confused about the bold part. I am forgetting something about taking the derivative of the natural number 'e'?
I know that d/dx e^x = x
so how does the ln b come behind e^x above?
what does (d/dx) e^f(x) equal to?
is (d/dx) e^f(x) = f '(x)* e^f(x) ?
if so then
1 + ln b
should come behind that because
d/dx (ln b)*x is equal to 1 + ln b
Please help me
thank you