2. Determine an unsimplified version of f′(x) without the help of Mathematica. You must write the names of more than 50%

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2 Determine An Unsimplified Version Of F X Without The Help Of Mathematica You Must Write The Names Of More Than 50 1 (119.3 KiB) Viewed 40 times

2. Determine an unsimplified version of f′(x) without the help of Mathematica. You must write the names of more than 50%1 of the "Differentiation Rules" for each problem below that you used. (a) (4) f(x)=(x3+3x2−6x+2)⋅(x2−x+3) (b) (4) f(x)=sin(x)1+x​ (c) (4) f(x)=3x7+2x​+xπ+35. 3. Suppose f(x)=2x3+3x2−12x+7. (a) (4) Determine the equation of the tangent line at x=2 for the graph of y=f(x). (b) (4) Determine the value(s) of x for which the tangent line is horizontal for the graph of y=f(x). 4. (6) Consider the graph given by x2−3xy+y2+1=0. Determine the equation of the tangent line at the point (2,1). 5. (4) Sketch a graph of a function that has a jump discontinuity at x=2 which is also left continuous at x=2. 6. Suppose that f(5)=1,f′(5)=9,g(5)=−6 and g′(5)=5. Suppose u(x)=f(x)g(x) and v(x)=g(x)f(x)​. Determine the following values. (a) (4) u′(5) (b) (4) v′(5)