Calculus and vectors (DERIVATIVE RULES)

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1. Differentiate the following functions:

a)f(x)=7x3 b) y = 12(x)^4/3 c)f(x)=3x25x d)y=(3x+2)2

2. Determine the equation to the graph of f(x)=x3+3x22 at x=1

3. Determine f '(x) of the following functions:

a)f(x)=4x7 b)f(x)=x3x2 c)f(x)=x2+5x+8 d) f(x)= 3x

e)f(x)=(2x)4 f)f(x)=x3

4. Differentiate each function:

a)h(x)=(2x+3)(x+4) b)f(x)=2x3+5x24x3.75 c)s=t2(t22t)

d) y=51x5+31x321x2+1 e)g(x)=5(x2)4

5. Differentiateh(x)=(x23x)(x5+2) using the product rule.