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f(x)=x^(2) f^(')(x)=

f(x)=x2 f(x)=x^{2} \newlinef′(x)= f^{\prime}(x)=

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Full solution

Q. f(x)=x2 f(x)=x^{2} \newlinef′(x)= f^{\prime}(x)=
  1. Identify Function: Identify the function to differentiate.\newlineThe function given is f(x)=x2f(x) = x^2.
  2. Apply Power Rule: Apply the power rule for differentiation.\newlineThe power rule states that the derivative of xnx^n with respect to xx is n∗xn−1n*x^{n-1}.\newlineSo, the derivative of x2x^2 with respect to xx is 2∗x2−12*x^{2-1}.
  3. Simplify Expression: Simplify the expression. 2x2−12x^{2-1} simplifies to 2x12x^{1} which is 2x2x.
  4. Write Final Answer: Write the final answer.\newlineThe derivative of f(x)=x2f(x) = x^2 with respect to xx is f′(x)=2⋅xf'(x) = 2\cdot x.

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