its 60x^{\frac{13}{2}}+27x^{\frac{7}{2}}+12x^{\frac{1}{2}}

Thank you for the clarification! It looks like you are referring to a different function for which you need the derivative. The function now appears to be:

\[
f(x) = 60x^{\frac{13}{2}} + 27x^{\frac{7}{2}} + 12x^{\frac{1}{2}}.
\]

Let's find the derivative of this new function using the power rule.

### Power Rule:
The power rule for differentiation states that:
\[
\frac{d}{dx} \left( x^n \right) = n \cdot x^{n-1}.
\]

### Step-by-Step Differentiation:

1. **Differentiate the first term:**
\[
\frac{d}{dx} \left( 60x^{\frac{13}{2}} \right) = 60 \cdot \frac{13}{2} x^{\frac{13}{2} - 1} = 60 \cdot \frac{13}{

Learn how to differentiate the function 60x^{13/2} + 27x^{7/2} + 12x^{1/2} step-by-step using the power rule for differentiation. This calculus problem covers key concepts in differentiation, making it suitable for students in Grades 11-12.

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