What is (\partial)/(\partial x)(e^{-xx}sin(3x+1)) ?

The answer to (\partial)/(\partial x)(e^{-xx}sin(3x+1)) is -2e^{-x^2}xsin(3x+1)+3e^{-x^2}cos(3x+1)

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(\partial)/(\partial x)(e^{-xx}sin(3x+1))

\frac{\partial}{\partial x} (e^{- xx} sin (3 x + 1))

- 2 e^{- x^{2}} x sin (3 x + 1) + 3 e^{- x^{2}} cos (3 x + 1)

Solution steps

\frac{\partial}{\partial x} (e^{- xx} sin (3 x + 1))

Simplify

e^{- xx} sin (3 x + 1) : e^{- x^{2}} sin (3 x + 1)

= \frac{\partial}{\partial x} (e^{- x^{2}} sin (3 x + 1))

Apply the Product Rule:

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

f = e^{- x^{2}}, g = sin (3 x + 1)

= \frac{\partial}{\partial x} (e^{- x^{2}}) sin (3 x + 1) + \frac{\partial}{\partial x} (sin (3 x + 1)) e^{- x^{2}}

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

\frac{\partial}{\partial x} (sin (3 x + 1)) = cos (3 x + 1) \cdot 3

= (- 2 e^{- x^{2}} x) sin (3 x + 1) + cos (3 x + 1) \cdot 3 e^{- x^{2}}

Simplify

= - 2 e^{- x^{2}} x sin (3 x + 1) + 3 e^{- x^{2}} cos (3 x + 1)

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

n = 1 \sum \infty \frac{( n + 6 )}{2}

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

2 x, \frac{x}{2}

\int \frac{x ^{2}}{( 1 - x ^{3} ) ^{7}} d x

What is (\partial)/(\partial x)(e^{-xx}sin(3x+1)) ?
The answer to (\partial)/(\partial x)(e^{-xx}sin(3x+1)) is -2e^{-x^2}xsin(3x+1)+3e^{-x^2}cos(3x+1)