List of top Mathematics Questions on Differentiation asked in GUJCET

The interval in which \( y = x^2 e^x \) is decreasing is _____
The total revenue in Rupees received from the sale of \( x \) units of a product is given by \( R(x) = 3x^2 + 36x + 5 \). The marginal revenue, when \( x = 15 \), is _____

If $e^y (x+1) = 1$, then find the value of $$ \frac{d^2 y}{dx^2} - \left(\frac{dy}{dx}\right)^2. $$ 

If \( y = \log_{2026}(\log_{2025} x) \), then \( \frac{dy}{dx} \)= _____
If \( x = a t^2, \; y = 2at \), then \( \frac{d^2 y}{dx^2} =\) _____
If \( x = a(1 - \cos\theta) \), \( y = a(\theta + \sin\theta) \), then \( \frac{dy}{dx} \) is: ...