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Popular >

derivative of 10xe^{-5x}

Solution

\frac{d}{d x} (10 x e^{- 5 x})

Solution

10 (e^{- 5 x} - 5 e^{- 5 x} x)

Solution steps

\frac{d}{d x} (10 x e^{- 5 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (x e^{- 5 x})

Apply the Product Rule:

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

f = x, g = e^{- 5 x}

= 10 (\frac{d x}{d x} e^{- 5 x} + \frac{d}{d x} (e^{- 5 x}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{- 5 x}) = - 5 e^{- 5 x}

= 10 (1 \cdot e^{- 5 x} + (- 5 e^{- 5 x}) x)

Simplify

= 10 (e^{- 5 x} - 5 e^{- 5 x} x)

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\int \frac{2 x + 1}{x ^{2} + 2 x + 37} d x

(\partial)/(\partial z)(x^2yz)

\frac{\partial}{\partial z} (x^{2} yz)

derivative of sin(x*sin(x))

\frac{d}{d x} (sin (x) \cdot sin (x))

Frequently Asked Questions (FAQ)

What is the derivative of 10xe^{-5x} ?
The derivative of 10xe^{-5x} is 10(e^{-5x}-5e^{-5x}x)
What is the first derivative of 10xe^{-5x} ?
The first derivative of 10xe^{-5x} is 10(e^{-5x}-5e^{-5x}x)