Question

$f\left( x\right) =\sum _{n=1}^{k}e^{nx}$ ve $f'\left( 0\right) =12.f\left( 0\right)$ ise k kactir?

Answer 1

$\dfrac{d}{dx}(e^{nx})=ne^{nx}$ oldugundan ve $e^0=1$ oldugundan $$1+2+\cdots+k=12k$$ esitligini elde ederiz.