Find d^2y dx^2 , where y= ( x^2 e^2 ) - Vidyadip

Question

Find $\frac{\text{d}^2\text{y}}{\text{dx}^2},$ where $\text{y}=\log\Big(\frac{\text{x}^2}{\text{e}^2}\Big)$

✓

Answer

Here
$\text{y}=\log\Big(\frac{\text{x}^2}{\text{e}^2}\Big)$
Differentiating w.r.t.x, we get
$\frac{\text{dy}}{\text{dx}}=\frac{1}{\frac{\text{x}^2}{\text{e}^2}}\times\frac{2\text{x}}{\text{e}^2}=\frac{2}{\text{x}}$
Differentiating w.r.t.x, we get
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{-2}{\text{x}^2}$

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.(2 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

Determine whether the following statement patterns are tautologies contradictions or contingencies : [p → (q → r)] ↔ [(p ∧ q) → r]

If the binary operation o is defined by a o b = a + b - ab on the set Q - {-1} of all rational numbers other than 1, shown that o is commutative on Q - [1].

Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On $\mathrm{Z}^{+}$, define * by a * $\mathrm{b}=\mathrm{a}$
Here, $\mathrm{Z}^{+}$denotes the set of all non-negative integers.

Diffrentiate the following w.r.t.x

$\sin ^2 x^2-\cos ^2 x^2$

The joint equation of the pair of lines passing through $(2,3)$ and parallel to the coordinate axes is ...

If $\text{A}=\begin{bmatrix}5&3&8\\2&0&1\\1&2&3\end{bmatrix}.$ Write the cofactor of element $a_{32}$.

Evaluate the following integrals:
$\int\cos^{-1}(\sin\text{x})\text{dx}$

Evaluate the following integrals:$\int\limits^\frac{\pi}{2}_0\cos^2\text{x}\text{ dx}$

Differentiate the following w. r. t. x.$\cos ^{-1}\left(2 x \sqrt{1-x^2}\right)$

If g (x) is a decreasing function on R and $\text{f}(\text{x})=\tan^{-1}[\text{g}(\text{x})].$ State whether f(x) is increasing or decreasing on R.