f(x)=(ax+b)sin(x)+(cx+d)cos(x) and (dy/dx)=xcos(x) find a , b , c , d


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Question Number 72250 by aliesam last updated on 26/Oct/19

$f (x) = (a x + b) s i n (x) + (c x + d) c o s (x)$ $a n d \frac{d y}{d x} = x c o s (x)$ $f i n d a, b, c, d$
Commented by kaivan.ahmadi last updated on 27/Oct/19

$\frac{d y}{d x} = a s i n x + (a x + b) c o s x + c . c o s x - (c x + d) s i n x =$ $(a - c x - d) s i n x + (a x + b + c) c o s x \Rightarrow$ ${\begin{cases} a - c x - d = 0 \\ a x + b + c = x \Rightarrow a = 1, b + c = 0 \Rightarrow b = - c \end{cases}$ $\Rightarrow 1 - c x - d = 0 \Rightarrow c x + d = 1 \Rightarrow c = 0, d = 1$ $\Rightarrow b = 0$ $\Rightarrow a = d = 1, b = c = 0$
Commented by kaivan.ahmadi last updated on 27/Oct/19

$f (x) = x s i n x + c o s x$
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