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CUET Mathematics 2026 PYQs14 May Shift 2. Free, no login required.

Applied Mathematics

past year questions, CUET Mathematics 2026 14 May Shift 2

Calculus

past year questions, Applied Mathematics, CUET Mathematics 2026 14 May Shift 2

Medium

applied

The second order derivative of the function y=log⁡(4x3+6)y=\log(4x^3+6) with respect to 'x' will be:

Solution

✅ Correct Option: 2

dydx=12x24x3+6=6x22x3+3\frac{dy}{dx}=\frac{12x^2}{4x^3+6}=\frac{6x^2}{2x^3+3}.

By the quotient rule, d2ydx2=12x(2x3+3)−6x2(6x2)(2x3+3)2=36x−12x4(2x3+3)2=12x(3−x3)(2x3+3)2\frac{d^2y}{dx^2}=\frac{12x(2x^3+3)-6x^2(6x^2)}{(2x^3+3)^2}=\frac{36x-12x^4}{(2x^3+3)^2}=\frac{12x(3-x^3)}{(2x^3+3)^2}.

Related questions:

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The second order derivative of which of the following functions is 5x5^x ?

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Match the LIST-I with LIST-II

LIST-I (Differential equation)LIST-II (Degree)
A.(dydx)2+1dydx=5\left(\dfrac{dy}{dx}\right)^2 + \dfrac{1}{\dfrac{dy}{dx}} = 5I.22
B.d3ydx3={3+(dydx)2}3/2\dfrac{d^3y}{dx^3} = \left\{3 + \left(\dfrac{dy}{dx}\right)^2\right\}^{3/2}II.44
C.d2ydx2=(dydx)5/4\dfrac{d^2y}{dx^2} = \left(\dfrac{dy}{dx}\right)^{5/4}III.11
D.yd2xdy2=y2+1y\dfrac{d^2x}{dy^2} = y^2 + 1IV.33

Choose the correct answer from the options given below:

2023: 7 June Shift 1

If t=e2xt = e^{2x} and log⁡et2\log_e t^2, then d2ydx2\frac{d^2y}{dx^2} is :

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