1. Find the derivatives of the following functions. You don't have
to simplify your answer. solution
(a) \(f(x)= (x^2+2x)(3x-5)\) (b)
\(f(x)= (5x-3x^5-x^7)(3x^2-5x)\)
2. Find the derivatives of the following functions. You don't have to
simplify your answer. solution
(a) \(f(x)= \dfrac{x^2+2x}{5x-1}\) (b)
\(f(x)= \dfrac{7+3x^5-x^7}{3x^2-5x}\)
3. If \( f(x) = \dfrac{x^2+3x+1}{2x-5}\), find the
value of \( f'(0)\). solution
4. Find \( F'(0) \) if \(F(x)=
(x^2+1)\, e^x \). solution
5. Find an equation of the tangent line to the curve \( y=1+xe^x\) at the
point \((0, 1)\).