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Use the appropriate differential rules to calculate the derivative. You may need to use some algebraic manipulation for certain problems. 3 1. f(x) = 2x³ 2 3x² + 5 -5/14 -5 + z 2. g(z) = 7z 4 3. f(s) = √√5 + √√s 3 +9

Use the appropriate differential rules to calculate the derivative. You may need to use some algebraic manipulation for certain problems. 3 1. f(x) = 2x³ 2 3x² + 5 -5/14 -5 + z 2. g(z) = 7z 4 3. f(s) = √√5 + √√s 3 +9

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.3: Rates Of Change
Problem 30E: If the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing...
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Problem7.. Use the appropriate differential rules to calculate the derivative. You may need to use some algebraic manipulation for certain problems. 3 2 1. f(x) 2x³ 3x² + 5 2. g(z) = 7z 3 3. f(s) = √√5 + √√s d ds 2 4. (4s - 3)² 5. d dr 6. = d dx -5/14 -5 + z (1 - 2r) (3r + 5) 2 x² +4x² 2 X 1/2 +9 Hint: Expand algebraically first.
Transcribed Image Text:Problem7.. Use the appropriate differential rules to calculate the derivative. You may need to use some algebraic manipulation for certain problems. 3 2 1. f(x) 2x³ 3x² + 5 2. g(z) = 7z 3 3. f(s) = √√5 + √√s d ds 2 4. (4s - 3)² 5. d dr 6. = d dx -5/14 -5 + z (1 - 2r) (3r + 5) 2 x² +4x² 2 X 1/2 +9 Hint: Expand algebraically first.
Problem6. It is common that we call the following differential rule the Power Rule: Here is the Sum/Difference Rule: d n -X d dx Here is the Constant Multiple Rule: d dx (kf) = k f(x) or f'(a). , x=a² n-1 = nx - (f ± g) = af ± -g for any differentiable functions fand g. d dx dx dx for any real number n. It is also common to use the following notation for the slope of the tangent line of f(x) at x = a : d -f for any differentiable functions fand real number k. dx Use the appropriate differential rules to compute the following. d 4. 1. Use the Power Rule to compute the derivative:- -X dx x=-2 2. Use the Power Rule to compute the derivative: ² dt 2/3 't=8 3. Use the Power Rule to compute the derivative:- -X 0.35 d dx 4. Compute f'(x)and find an equation of the tangent line to the graph at x = a f(x) = 5x − 32-√√x, a = 4
Transcribed Image Text:Problem6. It is common that we call the following differential rule the Power Rule: Here is the Sum/Difference Rule: d n -X d dx Here is the Constant Multiple Rule: d dx (kf) = k f(x) or f'(a). , x=a² n-1 = nx - (f ± g) = af ± -g for any differentiable functions fand g. d dx dx dx for any real number n. It is also common to use the following notation for the slope of the tangent line of f(x) at x = a : d -f for any differentiable functions fand real number k. dx Use the appropriate differential rules to compute the following. d 4. 1. Use the Power Rule to compute the derivative:- -X dx x=-2 2. Use the Power Rule to compute the derivative: ² dt 2/3 't=8 3. Use the Power Rule to compute the derivative:- -X 0.35 d dx 4. Compute f'(x)and find an equation of the tangent line to the graph at x = a f(x) = 5x − 32-√√x, a = 4
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