What is the derivative of a(2e^{-3x}x-3e^{-3x}x^2) ?

The derivative of a(2e^{-3x}x-3e^{-3x}x^2) is a(9e^{-3x}x^2-12e^{-3x}x+2e^{-3x})

What is the first derivative of a(2e^{-3x}x-3e^{-3x}x^2) ?

The first derivative of a(2e^{-3x}x-3e^{-3x}x^2) is a(9e^{-3x}x^2-12e^{-3x}x+2e^{-3x})

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Popular >

\frac{d}{d x} (a (2 e^{- 3 x} x - 3 e^{- 3 x} x^{2}))

a (9 e^{- 3 x} x^{2} - 12 e^{- 3 x} x + 2 e^{- 3 x})

Solution steps

\frac{d}{d x} (a (2 e^{- 3 x} x - 3 e^{- 3 x} x^{2}))

Take the constant out:

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

= a \frac{d}{d x} (2 e^{- 3 x} x - 3 e^{- 3 x} x^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= a (\frac{d}{d x} (2 e^{- 3 x} x) - \frac{d}{d x} (3 e^{- 3 x} x^{2}))

\frac{d}{d x} (2 e^{- 3 x} x) = 2 (- 3 e^{- 3 x} x + e^{- 3 x})

\frac{d}{d x} (3 e^{- 3 x} x^{2}) = 3 (- 3 e^{- 3 x} x^{2} + 2 e^{- 3 x} x)

= a (2 (- 3 e^{- 3 x} x + e^{- 3 x}) - 3 (- 3 e^{- 3 x} x^{2} + 2 e^{- 3 x} x))

Expand

2 (- 3 e^{- 3 x} x + e^{- 3 x}) - 3 (- 3 e^{- 3 x} x^{2} + 2 e^{- 3 x} x) : 9 e^{- 3 x} x^{2} - 12 e^{- 3 x} x + 2 e^{- 3 x}

= a (9 e^{- 3 x} x^{2} - 12 e^{- 3 x} x + 2 e^{- 3 x})

\frac{\partial}{\partial x} (- sin (4 x))

f (x) = x^{2} + 2 x + 3

\int 4 \frac{x}{( x + 2 ) ^{(\frac{1}{4})}} d x

x \to 1 - lim (3^{\frac{1}{x}})

\frac{\partial}{\partial y} (e^{x} + cos (y + z))

What is the derivative of a(2e^{-3x}x-3e^{-3x}x^2) ?
The derivative of a(2e^{-3x}x-3e^{-3x}x^2) is a(9e^{-3x}x^2-12e^{-3x}x+2e^{-3x})
What is the first derivative of a(2e^{-3x}x-3e^{-3x}x^2) ?
The first derivative of a(2e^{-3x}x-3e^{-3x}x^2) is a(9e^{-3x}x^2-12e^{-3x}x+2e^{-3x})