Question 366198
a) *[Tex \LARGE \frac{d}{dx}\left(x^3-6x^2+9x-1\right)=3x^2-12x+9]



b) *[Tex \LARGE \frac{d}{dx}\left(\frac{1}{2}x-\sqrt{x} \right)=\frac{d}{dx}\left(\frac{1}{2}x-x^{\frac{1}{2}} \right)=\frac{1}{2}-\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2}-\frac{1}{\sqrt{x}}]



c) *[Tex \LARGE \frac{d}{dx}\left(e^x-e^{-x}\right)=e^x-(-e^{-x})=e^{x}+e^{-x}=e^x+\frac{1}{e^x}]



d) *[Tex \LARGE \frac{d}{dx}\left(25\cos(x)-\sin(x)\right)=-25\sin(x)-\cos(x)]