Higher Order Derivatives

1. Find the first and second derivatives of the given function.  solution

(a) \(f(x)=-0.2x^2+0.5x+2\)

(b) \(f(x)=4x^5-8x^4+2x^3-7x+5 \)

2. Find the first and second derivatives of the function.  solution

(a) \(\displaystyle{f(x)= 3x^4-5x^2+1} \)   (b) \(\displaystyle{f(x)= (x+1)^4} \)   (c) \(\displaystyle{f(x)= (1- x^2)^7}\) 

3. Find the third derivative of the given function.   solution

(a) \(\displaystyle{f(x)= 2x^5+ 8x^2-3x+5}\)   (b) \(f(x)= \frac{1}{x}\)

4. Evaluate the following.  solution

(a) Find \(H''(0)\), given that \(H(x)=xe^x\).

(b) Find the fourth derivative of \(f(x)=\frac{3}{x}\).