derivative of (f(x)f(x))=cos(2x)

解答

\frac{d}{d x} ((f (x)) f (x)) = cos (2 x)

f (x) = \frac{sin ( 2 x ) + c _{1}}{2}, f (x) = - \frac{sin ( 2 x ) + c _{1}}{2}

求解步骤

\frac{d}{d x} ((f (x)) f (x)) = cos (2 x)

若

f^{^{'}} (x) = g (x)

则

f (x) = \int g (x) d x

f (x) f (x) = \int cos (2 x) d x

\int cos (2 x) d x = \frac{1}{2} sin (2 x) + c_{1}

f (x) f (x) = \frac{1}{2} sin (2 x) + c_{1}

整理

f (x) : f (x) = \frac{sin ( 2 x ) + 2 c _{1}}{2}, f (x) = - \frac{sin ( 2 x ) + 2 c _{1}}{2}

f (x) = \frac{sin ( 2 x ) + 2 c _{1}}{2}, f (x) = - \frac{sin ( 2 x ) + 2 c _{1}}{2}

化简

f (x) = \frac{sin ( 2 x ) + c _{1}}{2}, f (x) = - \frac{sin ( 2 x ) + c _{1}}{2}

\frac{x d x}{( 1 + x )} = \frac{d y}{y ^{3}}

y^{^{'}} - 2 y y^{^{'}} + e^{x} = 0

x e^{(x^{2})} + y y^{^{'}} = 0

y^{^{'}} = e^{- 5 y} (2 7 x - 4), y (0) = 1

y^{^{'}} = \frac{y ^{2} + 3}{( 2 x y )}