Differentiate `(e^(x)cos^(3)x sin^(2)x)` w.r.t. x.

1.	Differentiate `(e^(x)cos^(3)x sin^(2)x)` w.r.t. x.
Answer» Let `y=e^(x)cos^(3)xsin^(2)x." …(i)"` Taking logarithm on both sides of (i), we get `logy=x+3 log cos x+2 log sin x." …(ii)"` On differentiating both sides of (ii) w.r.t. x, we get `(1)/(y).(dy)/(dx)=1+(3)/(cosx).(-sinx)+(2)/(sinx).cosx` `rArr(dy)/(dx)=y.{1-3 tanx+2 cot x}` `=(e^(x)cos^(3)xsin^(2)x)(1-3tanx+2cotx).`

Discussion

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