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What is the derivative of 9−2x?

A) 9−2x
B) −2 · 9−2x
C) (ln 9) · 9−2x
D) −2(ln 9) · 9−2x

User Keya
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1 Answer

2 votes

Final answer:

The derivative of 9-2x is obtained by applying the power rule, resulting in -2 after differentiating the constant and the term with the exponent. The correct option is B: -2.

Step-by-step explanation:

The derivative of 9-2x with respect to x requires us to use the power rule for differentiation, which states that if you have a function of the form f(x) = x^n, the derivative f'(x) is nx^{n-1}.

Since 9 is a constant, its derivative is 0 and since -2x is essentially -2x^1, using the power rule, the derivative is -2 multiplied by x^{1-1} which simplifies to -2.

The correct answer is Option B: -2, which represents the derivative of the exponential function 9-2x.

User Ian P
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