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Differentiation of Exponential Functions

Differentiation of Exponential Functions. f(x + h) – f(x) h. lim h->0. f’(x) =. 10 x+h – 10 x h. lim h->0. =. 10 x x (10 h – 1) h. lim h->0. =. (10 h – 1) h. lim h->0. =. 10 x x. =. 10 x x 2.3026. Problem: Differentiate f(x) = 10 x from first principles.

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Differentiation of Exponential Functions

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  1. Differentiation of Exponential Functions f(x + h) – f(x) h lim h->0 f’(x) = 10x+h – 10x h lim h->0 = 10x x (10h – 1) h lim h->0 = (10h – 1) h lim h->0 = 10x x = 10x x 2.3026 Problem: Differentiate f(x) = 10x from first principles. Use your calculator to evaluate limit. Try h=0.0001

  2. Differentiation of Exponential Functions f(x + h) – f(x) h lim h->0 f’(x) = 2x+h – 2x h lim h->0 = 2x x (2h – 1) h lim h->0 = (2h – 1) h lim h->0 = 2x x = 2x x 0.6931 Problem: Differentiate f(x) = 2x from first principles. Use your calculator to evaluate limit. Try h=0.0001

  3. Differentiation of Exponential Functions f(x + h) – f(x) h lim h->0 f’(x) = 2.7x+h – 2.7x h lim h->0 = 2.7x x (2.7h – 1) h lim h->0 = (2.7h – 1) h lim h->0 = 2.7x x = 2.7x x 1.0006 Problem: Differentiate f(x) = 2.7x from first principles. Try h=0.0001 Use your calculator to evaluate limit.

  4. Differentiation of Exponential Functions f(x + h) – f(x) h lim h->0 f’(x) = ex+h – ex h lim h->0 = ex x (eh – 1) h lim h->0 = (eh – 1) h lim h->0 = ex x Problem: Differentiate f(x) = ex from first principles. Use your calculator to evaluate limit. Try h=0.0001 = ex x 1.0000

  5. Differentiation of Exponential Functions f(x + h) – f(x) h lim h->0 f’(x) = nex+h – nex h lim h->0 = nex x (eh – 1) h lim h->0 = (eh – 1) h lim h->0 = nex x = = nex x 1.0000 nex Problem: Differentiate f(x) = nex from first principles. Try h=0.0001 Use your calculator to evaluate limit.

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