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Let $y =ae^{t}$ , $x =b\sin{(e^{t})}$ , then $\frac{dy}{dx}$ equals

Option 1)
$\frac{a}{b}\cos(e^{t})$

Option 2)
$\frac{a}{b}\sec(e^{t})$

Option 3)
$\frac{a}{b}$

Option 4)
$\frac{b}{a}\cos(e^{t})$

Answers (1)

best_answer

As we have learnt,

Derivative of parametric function -

$Let\:\:x=f(t)orf(\theta )$

$y=f(t)\:or\:f(\theta )$

$Then$

$\frac{dy}{dx}=\frac{dy}{dt}\div \frac{dx}{dt}\:\:\:or\:\:\:\frac{dy}{d\theta }\div \frac{dx}{d\theta }$

- wherein

$Let\:\:y=sint$

$x=cost$

$\frac{dy}{dt}=cos\:t$

$\frac{dx}{dt}=-sin\:t$

$\Rightarrow \:\frac{dy}{dx}=-\frac{cost}{sint}$

$=\frac{-x}{y}$

$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{\frac{d}{dt}(ae^{t})}{\frac{d}{dt}b\sin (e^t)}= \frac{ae^t}{b\cos(e^t)\cdot e^t} = \frac{a}{b}\sec(e^t)$

Option 1)

$\frac{a}{b}\cos(e^{t})$

Option 2)

$\frac{a}{b}\sec(e^{t})$

Option 3)

$\frac{a}{b}$

Option 4)

$\frac{b}{a}\cos(e^{t})$

Posted by

Himanshu

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