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{:[f(x)=x^(11)],[f^(')(x)=]:}

f(x)=x11f′(x)= \begin{array}{l}f(x)=x^{11} \\ f^{\prime}(x)=\end{array}

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Find higher derivatives of rational and radical functionsright chevron icon

Full solution

Q. f(x)=x11f′(x)= \begin{array}{l}f(x)=x^{11} \\ f^{\prime}(x)=\end{array}
  1. Identify Function & Operation: Identify the function and the operation to be performed.\newlineWe are given the function f(x)=x11f(x) = x^{11} and we need to find its derivative, which is denoted by f′(x)f'(x).
  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⋅xn−1n\cdot x^{n-1}. Therefore, the derivative of f(x)=x11f(x) = x^{11} is f′(x)=11⋅x11−1f'(x) = 11\cdot x^{11-1}.
  3. Simplify Derivative: Simplify the expression for the derivative. f′(x)=11⋅x11−1f'(x) = 11\cdot x^{11-1} simplifies to f′(x)=11⋅x10f'(x) = 11\cdot x^{10}.
  4. Check for Errors: Check for any mathematical errors in the differentiation process.\newlineNo errors were made in applying the power rule and simplifying the expression.

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