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Calculate single-variable derivatives, indefinite integrals, and partial derivatives with fractional exponents and step-by-step solutions.
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The Power Rule states d/dx[xⁿ] = n·xⁿ⁻¹. Multiply the coefficient by the exponent, then reduce the exponent by 1. Works for any real n, including fractions like x^(1/2).
Use the same Power Rule. For x^(1/2) (square root), the derivative is (1/2)·x^(-1/2) = 1/(2√x). For x^(2/3), it becomes (2/3)·x^(-1/3).
For composite functions f(g(x)), the derivative is f'(g(x))·g'(x). Differentiate the outer function, keep the inner function, then multiply by the derivative of the inner function.