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

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

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

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

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derivative of

f (x) = \frac{sin ( x )}{e ^{x}}

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{x}{2}, 3 x^{2} - 1, 0, 0.5

- 9 x + 5

\frac{s ^{2} - 4}{s + 1}

\int \frac{1}{cos ( θ )} d θ

\int 2 y - x^{2} d x

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