Question

Use the derivative shortcuts from this chapter to calculate the derivatives. Make sure to either show all your work, or explain what shortcut you are using. 1. Figure out: a) d/dx (2^5) b) If f(x) = 8x^9; f'(x) =? c) d/dx (12 - 6x + x^3) d) d/dt (12 - 6x + x^3) e) If f(x) = -5/x^5; f'(x) =? 2. Find the derivative of each of the following functions two different (but correct) ways. First use the product and/or quotient rule as it is set up. Then simplify first and use only the constant multiple, sum, difference or power rules as needed. You should get the same answer both ways! a) x^2 * 3rd_root(x) b) (x^2+3x)/x c) x^2(x^3-10) 3. Consider the graph of a function f. Recall that the slope of the tangent line at a point x=a is equal to the instantaneous rate of change at x=a. The equation of the tangent line to the graph of a function f at x=3 is y = 12x - 28. (a) What is f(3)? What is f'(3)? (b) Given that f(x) = ax^2 + b, find the constants a and b.

          Use the derivative shortcuts from this chapter to calculate the derivatives. Make sure to either show all your work, or explain what shortcut you are using.
1. Figure out:
a) d/dx (2^5)
b) If f(x) = 8x^9; f'(x) =?
c) d/dx (12 - 6x + x^3)
d) d/dt (12 - 6x + x^3)
e) If f(x) = -5/x^5; f'(x) =?
2. Find the derivative of each of the following functions two different (but correct) ways.
First use the product and/or quotient rule as it is set up. Then simplify first and use only the constant multiple, sum, difference or power rules as needed. You should get the same answer both ways!
a) x^2 * 3rd_root(x)
b) (x^2+3x)/x
c) x^2(x^3-10)
3. Consider the graph of a function f. Recall that the slope of the tangent line at a point x=a is equal to the instantaneous rate of change at x=a. The equation of the tangent line to the graph of a function f at x=3 is y = 12x - 28.
(a) What is f(3)? What is f'(3)?
(b) Given that f(x) = ax^2 + b, find the constants a and b.

Use the derivative shortcuts from this chapter to calculate the derivatives. Make sure to either show all your work, or explain what shortcut you are using.
1. Figure out:
a) d/dx (2^5)
b) If f(x) = 8x^9; f'(x) =?
c) d/dx (12 - 6x + x^3)
d) d/dt (12 - 6x + x^3)
e) If f(x) = -5/x^5; f'(x) =?
2. Find the derivative of each of the following functions two different (but correct) ways.
First use the product and/or quotient rule as it is set up. Then simplify first and use only the constant multiple, sum, difference or power rules as needed. You should get the same answer both ways!
a) x^2 * 3rdroot(x)
b) (x^2+3x)/x
c) x^2(x^3-10)
3. Consider the graph of a function f. Recall that the slope of the tangent line at a point x=a is equal to the instantaneous rate of change at x=a. The equation of the tangent line to the graph of a function f at x=3 is y = 12x - 28.
(a) What is f(3)? What is f'(3)?
(b) Given that f(x) = ax^2 + b, find the constants a and b.

Added by Lynn S.

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