What is the derivative of (sin(2x)/(e^x)) ?

The derivative of (sin(2x)/(e^x)) is (2cos(2x)-sin(2x))/(e^x)

What is the first derivative of (sin(2x)/(e^x)) ?

The first derivative of (sin(2x)/(e^x)) is (2cos(2x)-sin(2x))/(e^x)

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

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

Solution steps

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

Apply the Quotient Rule:

(\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}}

Simplify

\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)})

What is the derivative of (sin(2x)/(e^x)) ?
The derivative of (sin(2x)/(e^x)) is (2cos(2x)-sin(2x))/(e^x)
What is the first derivative of (sin(2x)/(e^x)) ?
The first derivative of (sin(2x)/(e^x)) is (2cos(2x)-sin(2x))/(e^x)