The second order derivative of which of the following functions is 5^x ? Option 1: 5^x _e 5 Option 2: 5^x (_e 5)^2 Option 3: 5^x/(_e 5) Option 4: 5^x/((_e 5)^2)

Answer: 5^x/((_e 5)^2). Solution: If f''(x) = 5^x, then integrating once gives f'(x) = 5^x/(_e 5), and integrating again gives f(x) = 5^x/((_e 5)^2) (ignoring constants).

Applied Mathematics

Calculus

Medium

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

$5^x \log_e 5$

$5^x (\log_e 5)^2$

$\frac{5^x}{\log_e 5}$

$\frac{5^x}{(\log_e 5)^2}$

✅ Correct Option: 4

If $f''(x) = 5^x$ , then integrating once gives $f'(x) = \frac{5^x}{\log_e 5}$ , and integrating again gives $f(x) = \frac{5^x}{(\log_e 5)^2}$ (ignoring constants).

2026: 14 May Shift 2

The area of the region bounded by curves $y=x^2$ and line $y=4$ is:

2023: 11 Aug Shift 1

If x is real, the minimum value of $f(x) = x^2 - 8x + 20$ is :

2025: 2 June Shift 1

If $y = e^{\frac{1}{2}\log(1+ \tan^2 x)}$ , then $\frac{d^2y}{dx^2}$ is equal to:

2023: 11 Aug Shift 1

The degree of the differential equation $\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = k \frac{d^2 y}{dx^2}$ is :

2023: 7 June Shift 1

Area of the region bounded by the curve $x^2 = 4y$ , $x$ - axis and $x = 3$ is

2023: 11 Aug Shift 1

The value of the integral $\int_{-3}^{3} (x^3 - x) dx$ is :

The second order derivative of which of the following functions is 5x5^x5x ?

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

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