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Popular >

derivative of (3+2xe^{-2x})

Solution

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

Solution

- 4 e^{- 2 x} - 4 e^{- 2 x} x

Solution steps

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

Apply the Product Rule:

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

f = 3 + 2 x, g = e^{- 2 x}

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

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

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

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

Simplify

2 e^{- 2 x} + (- 2 e^{- 2 x}) (3 + 2 x) : - 4 e^{- 2 x} - 4 e^{- 2 x} x

= - 4 e^{- 2 x} - 4 e^{- 2 x} x

Popular Examples

derivative of pix^2

\frac{d}{d x} (π x^{2})

integral of (x^2+24x^3)/x

\int \frac{x ^{2} + 24 x ^{3}}{x} d x

derivative of arcsinh(5x^3-4x^2+11)

\frac{d}{d x} (arcsinh (5 x^{3} - 4 x^{2} + 11))

tangent of f(x)=2x-1+6/x ,\at x=2 tangent of

f (x) = 2 x - 1 + \frac{6}{x}, at x = 2

(\partial)/(\partial x)(A(e^{2x}+2e^{2x}x))

\frac{\partial}{\partial x} (A (e^{2 x} + 2 e^{2 x} x))

Frequently Asked Questions (FAQ)

What is the derivative of (3+2xe^{-2x}) ?
The derivative of (3+2xe^{-2x}) is -4e^{-2x}-4e^{-2x}x
What is the first derivative of (3+2xe^{-2x}) ?
The first derivative of (3+2xe^{-2x}) is -4e^{-2x}-4e^{-2x}x