If y=x+tan x,then cos ^2 x frac{d^2 y}{d x^2} | vedclass

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

Question

(D) Given,$y=x+	an x$. Differentiating with respect to $x$,we get: $\frac{dy}{dx} = 1 + \sec^2 x$. Differentiating again with respect to $x$,we get:

Vedclass · Accepted Answer

2y

Vedclass · Answer

(D) Given,$y=x+	an x$. Differentiating with respect to $x$,we get: $\frac{dy}{dx} = 1 + \sec^2 x$. Differentiating again with respect to $x$,we get: $\frac{d^2y}{dx^2} = 0 + 2 \sec x \cdot (\sec x 	an x) = 2 \sec^2 x 	an x$. Now,substitute this into the expression $\cos^2 x \frac{d^2y}{dx^2} + 2x$: $\cos^2 x (2 \sec^2 x 	an x) + 2x$. Since $\cos^2 x \cdot \sec^2 x = 1$,the expression simplifies to: $2 	an x + 2x = 2(x + 	an x)$. Since $y = x + 	an x$,the expression is equal to $2y$.

If $y=x+\tan x$,then $\cos ^2 x \frac{d^2 y}{d x^2}+2 x$ is equal to

Similar Questions

If $y=A \sin x+B \cos x$,then prove that $\frac{d^{2} y}{d x^{2}}+y=0$.

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

Let $g(x) = \log(f(x))$ where $f(x)$ is a twice differentiable positive function on $(0, \infty)$ such that $f(x+1) = x f(x)$. Then,for $N = 1, 2, 3, \ldots$,$g^{\prime \prime}\left(N+\frac{1}{2}\right) - g^{\prime \prime}\left(\frac{1}{2}\right) = $

If $f(x) = |x|^3$,show that $f''(x)$ exists for all real $x$,and find it.

If $y=5 \cos x-3 \sin x$,then $\frac{d^2 y}{d x^2}=$ . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module