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f(x)=x2f(x) = x^2. What is f′(x)f'(x) equal to ?

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Full solution

Q. f(x)=x2f(x) = x^2. What is f′(x)f'(x) equal to ?
  1. Identify function: Identify the function to differentiate. f(x)=x2f(x) = x^2 is a polynomial function where the exponent of xx is 22.
  2. Apply power rule: Apply the power rule for differentiation. The power rule states that the derivative of xnx^n with respect to xx is n∗x(n−1)n*x^{(n-1)}.
  3. Calculate derivative: Calculate the derivative using the power rule. f′(x)=2⋅x2−1=2⋅x1=2xf'(x) = 2\cdot x^{2-1} = 2\cdot x^1 = 2x

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