Help with simple derivative: how can f'(x) = constant * f(x) for function f(x)=2^x ?

[Famfeld]

how can f'(x) = a constant times f(x) for the function f(x) = 2^x as this textbook tries to explain. I am stumped. Please help a desperate parent.

Cheers,

Fam

 

[mmm4444bot]

Those constants in the image are rounded approximations of the natural logarithm of the base, in each case.

ln(2) ≈ 0.69

ln(10) ≈ 2.30

Here's the rule, for differentiating the exponential function f(x) = b^x:

f'(x) = b^x * ln(b)