Find d y d x if : y=1+x 2+x - Vidyadip

Question

Find $\frac{d y}{d x}$ if : $\mathrm{y}=\frac{1+x}{2+x}$

✓

Answer

$
y=\frac{1+x}{2+x}
$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{\mathrm{d} y}{\mathrm{~d} x} & =\frac{\mathrm{d}}{\mathrm{d} x}\left(\frac{1+x}{2+x}\right) \text { } \\
& =\frac{(2+x) \frac{\mathrm{d}}{\mathrm{d} x}(1+x)-(1+x) \frac{\mathrm{d}}{\mathrm{d} x}(2+x)}{(2+x)^2} \\
& =\frac{(2+x)(0+1)-(1+x)(0+1)}{(2+x)^2 \text { }} \\
\frac{\mathrm{d} y}{\mathrm{~d} x} & =\frac{(2+x)-(1+x)}{(2+x)^2}=\frac{2+x-1-x}{(2+x)^2}=\frac{1}{(2+x)^2}
\end{aligned}
$

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 Differentiation (p-1)→Differentiation (p-1) — all question types→Maths (commerce) STD 11 Commerce / Arts question papers→Maharashtra Board STD 11 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Express the following recurring decimals as a rational number: $0 . \overline{32}$

Express the following recurring decimals as a rational number: 3.5

For a G. P., if : sum of the first 3 terms is 125 and the sum of the next 3 terms is 27 , find the value of $r$.

Grace Fashion Boutique purchased a sewing machine at $₹ 25,000 /-$. After 3 years machine was sold at depreciated value of $₹ 18,225 /-$. Find the rate of depreciation.

Express the following recurring decimals as a rational number: $4 . \overline{18}$

Two cards are drawn from a pack of 52 cards. Find the probability that: both are from the same denomination.

Solve the inequations: $|2 x+7| \leq 25$

Find the single discount equivalent to a series discount of $10 \%, 20 \%$, and $15 \%$.

Express the following in the form of $a+i b, a, b \in R, i=\sqrt{ }-1$. State the values of $a$ and $b$ : $\frac{(2+i)}{(3-i)(1+2 i)}$

The odds against a certain event are $5: 2$ and the odds in favour of another independent event are $6: 5$. Find the chance that at least one of the events will happen.