If y =e^x+e^ x+ then d y d x = ? - Vidyadip

MCQ

If $y =e^x+e^{x+\ldots \infty}$ then $\frac{d y}{d x}=$ ?

✓
$\frac{y}{(1-y)}$
B
$\frac{1}{(y-1)}$
C
$\frac{1}{(1-y)}$
D
$\frac{y}{(y-1)}$

✓

Answer

Correct option: A.

$\frac{y}{(1-y)}$

(a) $\frac{y}{(1-y)}$
Explanation: We can write it as
$\Rightarrow y=e^{x+y}$
log y = (x + y) log e
Differentiating with respect to x,we get
$\begin{array}{l}\Rightarrow \frac{1}{y} \frac{d y}{d x}=1+\frac{d y}{d x} \\ \Rightarrow\left(\frac{1}{y}-1\right) \frac{d y}{d x}=1 \\ \Rightarrow \frac{d y}{d x}=1\left(\frac{y}{1-y}\right)\end{array}$

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