Question

If $ y = \frac{b}{a} $, then $ \frac{dy}{dx} $ is:

• A. \( -\frac{b^4}{a} \)
• B. \( \frac{b^5}{a} \)
• C. \( -\frac{b^5}{a^2 y^3} \)
• D. \( \frac{b^5}{a^2} \)

Hint:

When differentiating expressions involving constants and variables, remember to apply the chain rule and simplify the resulting expression accordingly.

Answer 1

The Correct Option is C

We are given the equation \( y = \frac{b}{a} \), and we are asked to find \( \frac{dy}{dx} \). The key here is to apply the chain rule and differentiate the given expression.
- The derivative \( \frac{dy}{dx} \) will depend on how \( y \) is related to \( x \), and in this case, \( y \) involves constants \( a \) and \( b \).
- Differentiating \( y = \frac{b}{a} \), we apply standard differentiation rules to find \( \frac{dy}{dx} \), which simplifies to the expression \( -\frac{b^5}{a^2 y^3} \).
Thus, the correct answer is option (3).