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Popular >

derivative of (6x^2+6e^{-x})

Solution

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

Solution

12 e^{- x} x - e^{- x} (6 x^{2} + 6)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (6 x^{2} + 6) = 12 x

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

= 12 x e^{- x} + (- e^{- x}) (6 x^{2} + 6)

Simplify

= 12 e^{- x} x - e^{- x} (6 x^{2} + 6)

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Frequently Asked Questions (FAQ)

What is the derivative of (6x^2+6e^{-x}) ?
The derivative of (6x^2+6e^{-x}) is 12e^{-x}x-e^{-x}(6x^2+6)
What is the first derivative of (6x^2+6e^{-x}) ?
The first derivative of (6x^2+6e^{-x}) is 12e^{-x}x-e^{-x}(6x^2+6)