Question

if alpha = sec 3 bita, then d alpha / d bita =​

Answer 1

Given:

$\rm \alpha = sec \:3 \beta$

To Find:

$\rm \dfrac{d \alpha }{d \beta }$

Answer:

$\rm \implies \dfrac{d \alpha }{d \beta } \\ \\ \rm \implies \dfrac{d }{d \beta } (sec \: 3 \beta ) \\ \\ \rm \dfrac{d}{dx} (sec \: x) = tan \: x.sec \: x : \\ \\ \rm \implies tan \: 3 \beta .sec \: 3 \beta \times \frac{d}{d \beta }(3 \beta ) \\ \\ \rm \implies 3tan \: 3 \beta .sec \: 3 \beta$

$\therefore$ $\boxed{\mathfrak{ \dfrac{d \alpha }{d \beta } = 3tan \: 3 \beta .sec \: 3 \beta }}$