Find the second order derivatives of the function given in Exerci… - Vidyadip

Question

Find the second order derivatives of the function given in Exercise:
$\text{x }\cos\text{x}$

✓

Answer

Let $\text{y}=\text{x}\cos\text{x}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\text{x}(-\sin\text{x})+\cos\text{x}.1=-\text{x}\sin\text{x}+\cos\text{x}$
and $\frac{\text{d}^2\text{y}}{\text{dx}^2}=-\text{x}\cos\text{x}-\sin\text{x}.1-\sin\text{x}=-\text{x}\cos\text{x}-2\sin\text{x}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\frac{(1+\sqrt{\text{x}})^2}{\sqrt{\text{x}}}\text{dx}$

Write the value of $\tan\Big(2\tan^{-1}\frac{1}{5}\Big)$

If f : A → B is an injection, such that range of f = {a}, determine the number of elements in A.

Determine whether $f(x)=-\frac{\pi}{2}+$ sin x is increasing or decreasing on $\left(-\frac{\pi}{3}, \frac{\pi}{3}\right)$

Prove the following Exercise:
$\int^{1}_{0}\text{x e}^{\text{x}}\ \text{dx}=1$

Find the set values of $\text{cosec}^{-1}\Big(\frac{\sqrt3}{2}\Big)$

Find AB, if $A=\left[\begin{array}{ll} {6} & {9} \\ {2} & {3} \end{array}\right] \text { and } B=\left[\begin{array}{lll} {2} & {6} & {0} \\ {7} & {9} & {8} \end{array}\right]$

Find the distance of the point (2, 3, 4) from the x-axis.

If A and B are two events such that $\text{P}(\text{A}\cap\text{B})=0.32$ and P (B) = 0.5, find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$.

If $A$ and $B$ are square matrices of the same order such that $AB = BA,$ then show that $(A + B)^2 = A^2 + 2AB + B^2.$