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differentiate this, and give your answer in the form of dy/dx

The derivative of the given equation \( x = \frac{10^y - 1}{2} \) with respect to \( y \), expressed as \( \frac{dy}{dx} \), is:

\[
\frac{dy}{dx} = \frac{10^y \cdot \ln(10)}{2}
\]

Do you have any questions or would you like further details on this solution?

Here are some related questions you might find useful:
1. How do you perform implicit differentiation step-by-step?
2. How can the chain rule be applied in this scenario?
3. What is the significance of the natural logarithm \( \ln(10) \) in the derivative?
4. How does the base of the exponential function affect the derivative?
5. Can you explain how the quotient rule could apply here?

**Tip:** When differentiating functions involving exponents, always remember to apply the chain rule for more complex cases like this one!

Learn how to differentiate the equation x = (10^y - 1)/2 with respect to y and find dy/dx. The solution involves using implicit differentiation and the chain rule, with detailed steps including the application of logarithms and the derivative of exponential functions. Suitable for students in Grades 11-12 studying calculus.

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