List of top Mathematics Questions on Derivatives asked in CUET (UG)

Match List-I with List-II:
List-IList-II
The derivative of \( \log_e x \) with respect to \( \frac{1}{x} \) at \( x = 5 \) is(I) -5
If \( x^3 + x^2y + xy^2 - 21x = 0 \), then \( \frac{dy}{dx} \) at \( (1, 1) \) is(II) -6
If \( f(x) = x^3 \log_e \frac{1}{x} \), then \( f'(1) + f''(1) \) is(III) 5
If \( y = f(x^2) \) and \( f'(x) = e^{\sqrt{x}} \), then \( \frac{dy}{dx} \) at \( x = 0 \) is(IV) 0
Choose the correct answer from the options given below :
\(\text{ If } \sin y = x \sin(a + y), \text{ then } \frac{dy}{dx} \text{ is:}\)
Match List-I with List-II:
List-I (Function)List-II (Derivative w.r.t. x)
(A) \( \frac{5^x}{\ln 5} \)(I) \(5^x (\ln 5)^2\)
(B) \(\ln 5\)(II) \(5^x \ln 5\) 
(C) \(5^x \ln 5\)(III) \(5^x\) 
(D) \(5^x\)(IV) 0 

Choose the correct answer from the options given below.