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Find the derivative of f(x) f(x) .\newlinef(x)=x4 f(x) = x^4 \newlineWrite your answer as a constant times a power of x x .\newlinef′(x)= f'(x) = ______

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Q. Find the derivative of f(x) f(x) .\newlinef(x)=x4 f(x) = x^4 \newlineWrite your answer as a constant times a power of x x .\newlinef′(x)= f'(x) = ______
  1. Identify function: Identify the function to differentiate.\newlineWe are given the function f(x)=x4f(x) = x^4 and we need to find its derivative with respect to xx.
  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 \cdot x^{n-1}. Here, n=4n=4, so we apply the power rule to find the derivative of x4x^4.
  3. Perform differentiation: Perform the differentiation using the power rule.\newlineUsing the power rule, the derivative of x4x^4 is 4⋅x4−14\cdot x^{4-1}, which simplifies to 4⋅x34\cdot x^3.
  4. Write final answer: Write the final answer.\newlineThe derivative of f(x)=x4f(x) = x^4 is f′(x)=4x3f'(x) = 4x^3.

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