What is the derivative of 1000(sin(x)(e^{-2x})) ?

The derivative of 1000(sin(x)(e^{-2x})) is 1000(e^{-2x}cos(x)-2e^{-2x}sin(x))

What is the first derivative of 1000(sin(x)(e^{-2x})) ?

The first derivative of 1000(sin(x)(e^{-2x})) is 1000(e^{-2x}cos(x)-2e^{-2x}sin(x))

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\frac{d}{d x} (1000 (sin (x)) (e^{- 2 x}))

1000 (e^{- 2 x} cos (x) - 2 e^{- 2 x} sin (x))

Solution steps

\frac{d}{d x} (1000 (sin (x)) (e^{- 2 x}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 1000 \frac{d}{d x} (sin (x) e^{- 2 x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = e^{- 2 x}

= 1000 (\frac{d}{d x} (sin (x)) e^{- 2 x} + \frac{d}{d x} (e^{- 2 x}) sin (x))

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

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

= 1000 (cos (x) e^{- 2 x} + (- 2 e^{- 2 x}) sin (x))

Simplify

= 1000 (e^{- 2 x} cos (x) - 2 e^{- 2 x} sin (x))

\int \frac{cos ( 9 x )}{1 + sin ^{2} ( 9 x )} d x

\int \frac{x}{x ^{2} + y} d x

\frac{d}{d t} (e^{\frac{t ^{2}}{2}})

\int \frac{4}{x ^{2} - 16} d x

\frac{d}{d x} (3 x^{4 x})

What is the derivative of 1000(sin(x)(e^{-2x})) ?
The derivative of 1000(sin(x)(e^{-2x})) is 1000(e^{-2x}cos(x)-2e^{-2x}sin(x))
What is the first derivative of 1000(sin(x)(e^{-2x})) ?
The first derivative of 1000(sin(x)(e^{-2x})) is 1000(e^{-2x}cos(x)-2e^{-2x}sin(x))