petergriffin198
Member
- Joined
- Sep 20, 2015
- Messages
- 43
- Gender
- Male
- HSC
- 2015
Help
Edit: 1 question
-
Finished your HSC? Check out our University Discussion, Non-School forums or help out next year's HSC students! -
YOU can help the next generation of students in the community! Share your trial papers and notes on our Notes & Resources page
3unit quick two questions (1 Viewer)
- Thread starter petergriffin198
- Start date
Help
Edit: 1 question
Silly Sausage
Well-Known Member
- Joined
- Dec 8, 2014
- Messages
- 594
- Gender
- Male
- HSC
- 2014
d/dx(e^(x))=e^x
If something is proportional to something else, say a to b, then a/b is a constant. I find this question a little hard to explain thoroughly, so I'll leave that for someone else to do, but I'll do an example.
Let's take the function y=2^x. We can use implicit differentiation to find the derivative:
y=2^x
ln(y)=ln(2^x)
ln(y)=x*ln(2)
Take derivative of both sides:
1/y*dy/dx=ln(2)
dy/dx=y*ln(2)
dy/dx=(2^x)*ln(2) (because y=2^x)
Now lets see whether a/b, or in this case f(x)/f'(x) is a constant
f(x)/f'(x)=(2^x)/((2^x)*ln(2))
= 1/ln(2)
1/ln(2) is a constant, so the f(x) is proportional to it's derivative, and the answer is c), the exponential function.
Let's take the function y=2^x. We can use implicit differentiation to find the derivative:
y=2^x
ln(y)=ln(2^x)
ln(y)=x*ln(2)
Take derivative of both sides:
1/y*dy/dx=ln(2)
dy/dx=y*ln(2)
dy/dx=(2^x)*ln(2) (because y=2^x)
Now lets see whether a/b, or in this case f(x)/f'(x) is a constant
f(x)/f'(x)=(2^x)/((2^x)*ln(2))
= 1/ln(2)
1/ln(2) is a constant, so the f(x) is proportional to it's derivative, and the answer is c), the exponential function.