derivada de (sin(2x)/(e^x))

Solución

\frac{d}{d x} (\frac{sin ( 2 x )}{e ^{x}})

\frac{2 cos ( 2 x ) - sin ( 2 x )}{e ^{x}}

Pasos de solución

\frac{d}{d x} (\frac{sin ( 2 x )}{e ^{x}})

Aplicar la regla del cociente:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( sin ( 2 x ) ) e ^{x} - \frac{d}{d x} ( e ^{x} ) sin ( 2 x )}{( e ^{x} ) ^{2}}

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

\frac{d}{d x} (e^{x}) = e^{x}

= \frac{cos ( 2 x ) \cdot 2 e ^{x} - e ^{x} sin ( 2 x )}{( e ^{x} ) ^{2}}

Simplificar

\frac{cos ( 2 x ) \cdot 2 e ^{x} - e ^{x} sin ( 2 x )}{( e ^{x} ) ^{2}} : \frac{2 cos ( 2 x ) - sin ( 2 x )}{e ^{x}}

= \frac{2 cos ( 2 x ) - sin ( 2 x )}{e ^{x}}

\frac{\partial}{\partial y} (2 x^{\frac{1}{2}} y^{\frac{1}{4}} + 7)

\int \frac{7 x ^{2} + x + 7}{( x ^{2} + 1 ) ^{2}} d x

\frac{\partial}{\partial y} (x^{2} ln (x y))

f (x) = 4 x - 3 x, (4, 10)

\frac{d}{d x} (e^{x + l n (x)})