If y=7^x(5x^3), then dy/dx is equal to: (consider _e x = x) Option 1: x.7^x-1[(5x)^3]+7^x/5x^3 Option 2: 7^x-1[x(5x^3)+7/5x^3] Option 3: 7^x[7\(5x^3)\+3/x] Option 4: x.7^x[x5x^3+7/5x^37]

The answer is '7^x[7\(5x^3)\+3/x]'. View full solution:

CUET Mathematics - If y=7^x(5x^3), then dy/dx is equal to: (consider _e x = x) | PYQs + Solutions

CUET Mathematics 2026 12th May Shift 2

Calculus

Medium

applied

$x.7^{x-1}[\log(5x)^3]+\dfrac{7^x}{5x^3}$

$7^{x-1}\left[x\log(5x^3)+\dfrac{7}{5x^3}\right]$

$7^x\left[\log7\{\log(5x^3)\}+\dfrac{3}{x}\right]$

$x.7^x\left[x\log5x^3+\dfrac{7}{5x^3}\log7\right]$

✅ Correct Option: 3

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If $y = \frac{1}{1+x^{b-a}+x^{c-a}} + \frac{1}{1+x^{c-b}+x^{a-b}} + \frac{1}{1+x^{a-c}+x^{b-c}}$ then $\frac{d^2y}{dx^2}$ is

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Match List-I with List-II

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(B) $g(x) = [x]$ , $[x]$ denotes the greatest integer function	(II) is continuous at $x = 0$
(C) $h(x) = \begin{cases} \dfrac{\sin x}{x} & , x < 0 \\ x+1 & , x \geq 0 \end{cases}$	(III) is discontinuous at $x = -2$
(D) $p(x) = \begin{cases} \dfrac{x}{\left\vert x \right\vert} & , x < 0 \\ -1 & , x \geq 0 \end{cases}$	(IV) is discontinuous at $x = 1$

Choose the correct answer from the options given below: