3unit quick two questions (1 Viewer)

[petergriffin198]

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[Silly Sausage]

d/dx(e^(x))=e^x

 

[calamebe]

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.