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For f(x) = 2": %3D f'(x) = 2" In(2) f'(2) - For g(x) = 3- 10": g'(x) = g'(3) 2

For f(x) = 2": %3D f'(x) = 2" In(2) f'(2) - For g(x) = 3- 10": g'(x) = g'(3) 2

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The Power Rule lets us differentiate power functions, which have the form x", where the exponent a is a constant. (For example, we can use the Power rule to find the derivatives of x°, x7 and x-.) 3 However, the Power Rule DOES NOT tell us how to take derivatives of function that have the form a", where the exponent is the variable and the base is a constant. Instead, we have an Exponential Rule: d -[a*] = a In(a) dx So, for example, the derivative of 5 is 5" In(5). Use this Exponential Rule to answer the following questions: For f(x) = 2": f'(x) = 2" In(2) f'(2) 2 For g(x) = 3 · 10": %3D = (x),6 g'(3) ~
Transcribed Image Text:The Power Rule lets us differentiate power functions, which have the form x", where the exponent a is a constant. (For example, we can use the Power rule to find the derivatives of x°, x7 and x-.) 3 However, the Power Rule DOES NOT tell us how to take derivatives of function that have the form a", where the exponent is the variable and the base is a constant. Instead, we have an Exponential Rule: d -[a*] = a In(a) dx So, for example, the derivative of 5 is 5" In(5). Use this Exponential Rule to answer the following questions: For f(x) = 2": f'(x) = 2" In(2) f'(2) 2 For g(x) = 3 · 10": %3D = (x),6 g'(3) ~
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