See attached file for full problem description.
1. Find dy for each of the following functions.
d) y=square root 5x - square root x/5
2. a) Find the slope of the tangent to the curve y=4x^3-3x^2+1 at the point where x=-1.
b) Find the equation of the tangent to the curve y=2x-x2 that is perpendicular to the line x+4y-8=0.
3. If f(x)=320, find the derivative of f(x). Clearly give reason(s) for the answer.
4. Given f(x)=x3-1/2x^2+1. Find the value of x where dy =4.
The solution shows how to apply basic rules to calculate the derivatives of functions and equation of tangent line in detail.