If y=x+e^x, find d^2x dy^2 . - Vidyadip

Question

If $\text{y}=\text{x}+\text{e}^\text{x},$ find $\frac{\text{d}^2\text{x}}{\text{dy}^2}.$

✓

Answer

Here,
$\text{y}=\text{x}+\text{e}^\text{x}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=1+\text{e}^\text{x}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{1}{1+\text{e}^\text{x}}$
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{-\text{e}^\text{x}}{(1+\text{e}^\text{x})^2}$
$\frac{\text{dx}}{\text{dy}}=-\frac{-\text{e}^\text{x}}{(1+\text{e}^\text{x})^3}$

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

If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
$\text{x}=\cos\theta-\cos2\theta,\text{y}=\sin\theta-\sin2\theta$

If $A$ is a non$-$singular square matrix such that $\text{A}^{-1}=\begin{bmatrix} 5 & 3 \\ -2 & -1 \end{bmatrix},$ then find $(A^T)^{-1}.$

Write the slop of the normal to the curve $\text{y}=\frac{1}{\text{x}}$ at the point $\Big(3,\frac{1}{3}\Big).$

Define a commutative binary operation on a set.

If function $F (x)=\frac{\sin (10 x)}{x}, x \neq 0$, is continuous at $x=0$. Then find the value of $F (0)$.

Find the principal value of the following:
$\cos^{-1}\Big(\tan\frac{3\pi}{4}\Big)$

Write the value of $\cot^{-1}(-\text{x})$ for all $\text{x}\in\text{R}$ in terms of $\cot^{-1}\text{x}$

If $\int\limits^{\text{a}}_03\text{x}^2\text{ dx}=8,$ Write the value of a.

Evaluate the following determinant:
$\begin{vmatrix}\text{a}&\text{h}&\text{g}\\\text{h}&\text{b}&\text{f}\\\text{g}&\text{f}&\text{c}\end{vmatrix}$

Find the vector equation of the plane which is at a distance of 5 units from the orgin and its normal vector is $2\hat{\text{i}}+3\hat{\text{j}}+6\hat{\text{k}}.$