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Popular >

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

Solution

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

Solution

- 7 e^{- 3 x} - 6 e^{- 3 x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 e^{- 3 x} + (- 3 e^{- 3 x}) (3 + 2 x) : - 7 e^{- 3 x} - 6 e^{- 3 x} x

= - 7 e^{- 3 x} - 6 e^{- 3 x} x

Popular Examples

9y^{''}-12y^'+4y=0

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0

tangent of (5x^2)/((3-4x)^4)tangent of

\frac{5 x ^{2}}{( 3 - 4 x ) ^{4}}

laplacetransform sin(3t)cos(3t)laplace transform

sin (3 t) cos (3 t)

tangent of f(x)= 1/(2sqrt(x)),\at x=1 tangent of

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

2y^{''}+11y^'-6y=0

2 y^{^{''}} + 11 y^{^{'}} - 6 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of (3+2xe^{-3x}) ?
The derivative of (3+2xe^{-3x}) is -7e^{-3x}-6e^{-3x}x
What is the first derivative of (3+2xe^{-3x}) ?
The first derivative of (3+2xe^{-3x}) is -7e^{-3x}-6e^{-3x}x