If f(x) = sin x + cos x, then fleft(frac{pi}{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $f(x) = \sin x + \cos x$. First derivative: $f'(x) = \cos x - \sin x$. Second derivative: $f''(x) = -\sin x - \cos x$. Third derivative: $f'

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Given $f(x) = \sin x + \cos x$. First derivative: $f'(x) = \cos x - \sin x$. Second derivative: $f''(x) = -\sin x - \cos x$. Third derivative: $f'''(x) = -\cos x + \sin x$. Fourth derivative: $f^{(iv)}(x) = \sin x + \cos x$. Now, calculate the value at $x = \frac{\pi}{4}$: $f\left(\frac{\pi}{4}ight) = \sin\left(\frac{\pi}{4}ight) + \cos\left(\frac{\pi}{4}ight) = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2}$. Similarly, $f^{(iv)}\left(\frac{\pi}{4}ight) = \sin\left(\frac{\pi}{4}ight) + \cos\left(\frac{\pi}{4}ight) = \sqrt{2}$. Therefore, $f\left(\frac{\pi}{4}ight) f^{(iv)}\left(\frac{\pi}{4}ight) = \sqrt{2} 	imes \sqrt{2} = 2$.

If $f(x) = \sin x + \cos x$, then $f\left(\frac{\pi}{4}\right) f^{(iv)}\left(\frac{\pi}{4}\right)$ is equal to

Similar Questions

If $e^y(x+1)=1$,then $\frac{d^2 y}{d x^2} = $ . . . . . .

If $f(x) = \sin(\sin x)$ and $f''(x) + \tan x f'(x) + g(x) = 0$,then $g(x)$ is

If $y = \frac{A}{x} + B x^2$, then $x^2 \frac{d^2 y}{d x^2} =$

If $y = \cos^{2} \frac{3x}{2} - \sin^{2} \frac{3x}{2}$,then $\frac{d^{2}y}{dx^{2}}$ is

If $x^2y + y^3 = 2$,then the value of $\frac{d^2y}{dx^2}$ at the point $(1, 1)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module