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Popular >

derivative of (x^2+4e^{-2x})

Solution

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

Solution

2 e^{- 2 x} x - 2 e^{- 2 x} (x^{2} + 4)

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + 4, g = e^{- 2 x}

= \frac{d}{d x} (x^{2} + 4) e^{- 2 x} + \frac{d}{d x} (e^{- 2 x}) (x^{2} + 4)

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

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

= 2 x e^{- 2 x} + (- 2 e^{- 2 x}) (x^{2} + 4)

Simplify

= 2 e^{- 2 x} x - 2 e^{- 2 x} (x^{2} + 4)

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\frac{d}{d x} (cot^{2} (x) csc (x))

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+4e^{-2x}) ?
The derivative of (x^2+4e^{-2x}) is 2e^{-2x}x-2e^{-2x}(x^2+4)
What is the first derivative of (x^2+4e^{-2x}) ?
The first derivative of (x^2+4e^{-2x}) is 2e^{-2x}x-2e^{-2x}(x^2+4)