What is the derivative of the function f(x) = 2x²?

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Multiple Choice

What is the derivative of the function f(x) = 2x²?

To determine the derivative of the function \( f(x) = 2x^2 \), you apply the power rule of differentiation. The power rule states that if you have a function in the form of \( ax^n \), the derivative is given by \( nax^{n-1} \). In this case, the function can be identified as \( f(x) = 2x^2 \), where \( a = 2 \) and \( n = 2 \). Applying the power rule: 1. Multiply the exponent (2) by the coefficient (2), which gives \( 2 \times 2 = 4 \). 2. Then subtract 1 from the exponent (2), yielding \( 2 - 1 = 1 \). So, the derivative is \( f'(x) = 4x^{1} \), which simplifies to \( f'(x) = 4x \). This derivation shows that the correct answer is indeed the one that states \( f'(x) = 4x \), clearly demonstrating the application of the power rule to find the derivative of the function.

To determine the derivative of the function ( f(x) = 2x^2 ), you apply the power rule of differentiation. The power rule states that if you have a function in the form of ( ax^n ), the derivative is given by ( nax^{n-1} ).

In this case, the function can be identified as ( f(x) = 2x^2 ), where ( a = 2 ) and ( n = 2 ). Applying the power rule:

  1. Multiply the exponent (2) by the coefficient (2), which gives ( 2 \times 2 = 4 ).

  2. Then subtract 1 from the exponent (2), yielding ( 2 - 1 = 1 ).

So, the derivative is ( f'(x) = 4x^{1} ), which simplifies to ( f'(x) = 4x ).

This derivation shows that the correct answer is indeed the one that states ( f'(x) = 4x ), clearly demonstrating the application of the power rule to find the derivative of the function.

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