If y = x|x|, find dy dx for x 0<0. - Vidyadip

Question

If y = x|x|, find $\frac{\text{dy}}{\text{dx}}\text{ for x 0}<0.$

✓

Answer

We have, y = x|x|
$\Rightarrow\text{y}=\text{x}(-\text{x})\big(\because\text{x}>0\big)$
$\Rightarrow\text{y}=-\text{x}^2$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}(-\text{x}^2)$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=-2\text{x}$

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 Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\text{x}=2\text{ at},\text{y}=\text{at}^2,$ where a is a constant, then find $\frac{\text{d}^2\text{y}}{\text{dx}^2}\text{ at}\text{ x}=\frac{1}{2}.$

Integrate the function: $\frac{{{{\sin }^{ - 1}}x}}{{\sqrt {1 - {x^2}} }}$

Give example of matrices:
A and B such that AB = 0 but BA ≠ 0

Find the interval where function $f(x)=x^3-3 x$ is decreasing.

If A and B are two events write the expression for the probability of occurrence of exactly one of two events.

Let $S = \{a, b, c\}$ and $T = \{1, 2, 3\}.$ Find $F^{–1}$ of the following functions $F$ from $S$ to $T,$ if it exists:
$F = \{(a, 3), (b, 2), (c, 1)\}$

Write the direction cosines of the vectors $-2\hat{\text{i}}+\hat{\text{j}}-5\hat{\text{k}}$.

If $A = [a_{ij}]$ is a skew-symmetric matrix, then write the value of $\sum\limits_\text{i}\sum\limits_\text{j}\text{a}_\text{ij}.$

Evaluate the following definite integrals:
$\int_{0}^\limits{\frac{\pi}{2}}\text{x}^2\cos\text{x}\text{ dx}$

Using determinants prove that the points $(a, b), (a', b)$ and $(a - a', b - b')$ are collinear if $ab' = a'b$.