If y= x , show that d^2y dx^2 = 2 -3 x^3 . - Vidyadip

Question

If $\text{y}=\frac{\log\text{x}}{\text{x}},$ show that $\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{2\log\text{x}-3}{\text{x}^3}.$

✓

Answer

Here,
$\text{y}=\frac{\log\text{x}}{\text{x}},$
Differentiating w.r.t.x, we get
$\frac{\text{d}\text{y}}{\text{dx}}=\frac{1-\log\text{x}}{\text{x}^2}$
Differentiating w.r.t.x, we get
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{-\text{x}-2\text{x}(1-\log\text{x})}{\text{x}^4}$
$=\frac{-\text{x}-2\text{x}+2\text{x}\log\text{x}}{\text{x}^4}$
$=\frac{-3+2\log\text{x}}{\text{x}^3}$
$=\frac{2\log\text{x}-3}{\text{x}^3}$
Hence proved

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 "Solve the Following Question.(3 Marks)" from Higher Order Derivatives→Higher Order Derivatives — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If the position vectors of the points A(3, 4), B(5, -6) and C(4, -1) are $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ respectively, compute $\vec{\text{a}}+2\vec{\text{b}}-3\vec{\text{c}}$.

A bag contains $1$ white and $6$ red balls, and a second bag contains $4$ white and $3$ red balls. One of the bags is picked up at random and a ball is randomly drawn from it, and is found to be white in colour. Find the probability that the drawn ball was from the first bag.

In a family, the husband tells a lie in 30% cases and the wife in 35% cases. Find the probability that both contradict each other on the same fact.

Find the equation of the plane passing through (a, b, c) and parallel to the plane $\vec{\text{r}}\cdot(\text{i}+\hat{\text{j}}+\hat{\text{k}})=2$

Find the vector equations of the following planes in scalar product form $(\vec{\text{r}}\cdot\vec{\text{n}}=\text{d}):$
$\vec{\text{r}}=\hat{\text{i}}-\hat{\text{j}}+\lambda(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}})+\mu(4\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}})$

Find the slopes of the tangent and the normal to the following curves at the indicated points:
$\text{y}=2\text{x}^2+3\sin\text{x}\ \text{at}\text{ x}=0$

Evaluate the following intregals:
$\int\frac{1}{\sin^2\text{x}-\sin2\text{x}}\ \text{dx}$

Find the area of the parallelogram determinrd by the vectors:
$\hat{\text{i}}-3\hat{\text{j}}+\hat{\text{k}}$ and $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}.$

Suppose that $80 \%$ of all families own a television set. If 10 families are interviewed at random, find the probability that at most three families own a television set.

Evaluate $\sin\Big(\tan^{-1}\frac{3}{4}\Big).$