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Let h(x)=x^((5)/(2)). h^(')(x)=

Let h(x)=x52 h(x)=x^{\frac{5}{2}} .\newlineh′(x)= h^{\prime}(x)=

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Full solution

Q. Let h(x)=x52 h(x)=x^{\frac{5}{2}} .\newlineh′(x)= h^{\prime}(x)=
  1. Apply Power Rule: To find the derivative of h(x)=x52h(x) = x^{\frac{5}{2}}, we will use the power rule for differentiation. The power rule states that if h(x)=xnh(x) = x^n, then h′(x)=n⋅xn−1h'(x) = n \cdot x^{n-1}.
  2. Calculate New Exponent: Applying the power rule to h(x)=x52h(x) = x^{\frac{5}{2}}, we get h′(x)=(52)⋅x(52−1)h'(x) = \left(\frac{5}{2}\right)\cdot x^{\left(\frac{5}{2}-1\right)}.
  3. Final Derivative: Subtract 11 from the exponent (5/2)(5/2) to get the new exponent for xx. (5/2)−1=(5/2)−(2/2)=(3/2)(5/2) - 1 = (5/2) - (2/2) = (3/2).
  4. Final Derivative: Subtract 11 from the exponent (5/2)(5/2) to get the new exponent for xx. (5/2)−1=(5/2)−(2/2)=(3/2)(5/2) - 1 = (5/2) - (2/2) = (3/2).Now we have h′(x)=(5/2)⋅x(3/2)h'(x) = (5/2)\cdot x^{(3/2)}. This is the derivative of h(x)h(x) with respect to xx.

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