A) \[\frac{{{e}^{ax}}[a\sin (bx+c)+b\cos (bx+c)]}{{{\sin }^{2}}(bx+c)}\]
B) \[\frac{{{e}^{ax}}[a\sin (bx+c)-b\cos (bx+c)]}{\sin (bx+c)}\]
C) \[\frac{{{e}^{ax}}[a\sin (bx+c)-b\cos (bx+c)]}{{{\sin }^{2}}(bx+c)}\]
D) None of these
Correct Answer: C
Solution :
\[\frac{d}{dx}\left( \frac{{{e}^{ax}}}{\sin (bx+c)} \right)\]\[=\frac{a{{e}^{ax}}\sin (bx+c)-b{{e}^{ax}}\cos (bx+c)}{{{\{\sin (bx+c)\}}^{2}}}\] \[=\frac{{{e}^{ax}}[a\sin (bx+c)-b\cos (bx+c)]}{{{\sin }^{2}}(bx+c)}\].You need to login to perform this action.
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