What is the derivative of (9x^2-18x+18e^{-6x}) ?

The derivative of (9x^2-18x+18e^{-6x}) is -54e^{-6x}x^2+126e^{-6x}x-126e^{-6x}

What is the first derivative of (9x^2-18x+18e^{-6x}) ?

The first derivative of (9x^2-18x+18e^{-6x}) is -54e^{-6x}x^2+126e^{-6x}x-126e^{-6x}

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Popular >

\frac{d}{d x} ((9 x^{2} - 18 x + 18) e^{- 6 x})

- 54 e^{- 6 x} x^{2} + 126 e^{- 6 x} x - 126 e^{- 6 x}

Solution steps

\frac{d}{d x} ((9 x^{2} - 18 x + 18) e^{- 6 x})

Apply the Product Rule:

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

f = 9 x^{2} - 18 x + 18, g = e^{- 6 x}

= \frac{d}{d x} (9 x^{2} - 18 x + 18) e^{- 6 x} + \frac{d}{d x} (e^{- 6 x}) (9 x^{2} - 18 x + 18)

\frac{d}{d x} (9 x^{2} - 18 x + 18) = 18 x - 18

\frac{d}{d x} (e^{- 6 x}) = - 6 e^{- 6 x}

= (18 x - 18) e^{- 6 x} + (- 6 e^{- 6 x}) (9 x^{2} - 18 x + 18)

Simplify

(18 x - 18) e^{- 6 x} + (- 6 e^{- 6 x}) (9 x^{2} - 18 x + 18) : - 54 e^{- 6 x} x^{2} + 126 e^{- 6 x} x - 126 e^{- 6 x}

= - 54 e^{- 6 x} x^{2} + 126 e^{- 6 x} x - 126 e^{- 6 x}

\frac{d}{d x} (\frac{x ^{2} + 4}{x + 5})

\int_{1}^{e^{4}} \frac{ln ^{2} ( x ^{2} )}{x} d x

\int_{- 1}^{2} x^{3} d x

x \to \infty lim (0. 6^{x})

f (x) = ln (x)

What is the derivative of (9x^2-18x+18e^{-6x}) ?
The derivative of (9x^2-18x+18e^{-6x}) is -54e^{-6x}x^2+126e^{-6x}x-126e^{-6x}
What is the first derivative of (9x^2-18x+18e^{-6x}) ?
The first derivative of (9x^2-18x+18e^{-6x}) is -54e^{-6x}x^2+126e^{-6x}x-126e^{-6x}