D/dx ( e^ax/sin(bx+c) )=ae^axsin(bx+c) be^axcos(bx+c)/{ sin(bx+c) }^2 =e^ax[a sin(bx+c) b cos(bx+c)]/sin^2(bx+c) ...

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Quotient Rule of Differentiation

d/dx [ eax/si...

Question

$\frac{d}{d x} [\frac{e^{a x}}{s i n (b x + c)}] =$

= \frac{e^{a x} [a s i n (b x + c) + b c o s (b x + c)]}{s i n^{2} (b x + c)}

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= \frac{e^{a x} [a s i n (b x + c) - b c o s (b x + c)]}{s i n (b x + c)}

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= \frac{e^{a x} [a s i n (b x + c) - b c o s (b x + c)]}{s i n^{2} (b x + c)}

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None of these

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Solution

The correct option is C $= \frac{e^{a x} [a s i n (b x + c) - b c o s (b x + c)]}{s i n^{2} (b x + c)}$
$\frac{d}{d x} (\frac{e^{a x}}{s i n (b x + c)})$ $= \frac{a e^{a x} s i n (b x + c) - b e^{a x} c o s (b x + c)}{{s i n (b x + c)}^{2}} = \frac{e^{a x} [a s i n (b x + c) - b c o s (b x + c)]}{s i n^{2} (b x + c)}$

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