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.
The condition on a and b, such that for \(y = \frac{a}{x}-\frac{b}{x²}\), \(\frac{dy}{dx} =0\) at x=1 is:
If cosy = xcos(a + y), then \(\frac{dy}{dx}\) =
If y = Asinx + Bcosx, Where A and B are constants, then \(\frac{d^2y}{dx^2}\) is equal to :
If xy = e(x-y), then the value of \(\frac{dy}{dx}\) at (1, 1) is :
Match List I with List II
List I
(Functions)		List II
(Derivatives)
A.f(x)=sin-1xI.\(\frac{1}{1+x^2}\), x ∈ R
B.f(x)=tan-1xII.\(\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
C.f(x)=cos-1xIII.\(-\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
D.f(x)=sin-1xIV.\(-\frac{1}{1+x^2}\), x ∈ R
Choose the correct answer from the options given below :
If \(x^{\frac{3}{4}}+y^{\frac{3}{4}}=a^{\frac{3}{4}}\) (a is a constant) then \(\frac{dy}{dx}\) is equal to :
Match List I with List II
LIST I LIST II
A.\(\frac{d}{dx} [tan^{-1} (\frac{3x-x^3}{1-3x^2})]\)I.\(\frac{3}{1+x^2}\)
B.\(\frac{d}{dx}[cos^{-1}(\frac{1-x^2}{1+x^2})]\)II.\(\frac{-3}{1+x^2}\)
C.\(\frac{d}{dx}[cos^{-1} (\frac{2x}{1+x^2})]\)III.\(\frac{-2}{1+x^2}\)
D.\(\frac{d}{dx}[cot^{-1}(\frac{3x-x^3}{1-3x^2})]\)IV.\(\frac{2}{1+x^2}\)
Choose the correct answer from the options given below:
If y = \(10^{10^x}\), then \(\frac{dy}{dx}\) is :
The derivative \(\frac{\mathrm dy}{\mathrm d x}\) ,if \(x=a(\theta -sin\theta),y=a(1+cos\theta)\) is :
If \(e^y(x+2)=10\), then \(\frac{d^2y}{dx^2}\) is equal to:
If \(x=3at^2\), \(y=3at^4\) then \(\frac{dy}{dx}\) is:
If \(y = log(\frac{x^5}{e^5})\), then \(\frac{d^2y}{dx^2}\) is,
Derivative of \(2x^2\) with respect to \(5x^4\) is:
If \(x = \sqrt{a^{sin^{-1} t}}\), \(y = \sqrt{a^{ cos^{-1}t}}\) then \(\frac{dy}{dx}\) is:
If y = x + tan x, then value of \(\frac{d^2y}{dx^2}\) at \(x= \frac{\pi}{4}\) is:
Differential coefficient of see (\(tan^{-1} x\)) with respect to x is:
If \(y=\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+}}}}.....+\) then \(\frac{dy}{dx}\) is :
The derivative of \(f (cot x)\) with respect to \(g (cosec x)\) at \(x=\frac{π}{4}\) (where \(f'(1)=2.g'(\sqrt2)=4\)) is: