What is the derivative of e^{-10x}-10e^{-10x}x ?

The derivative of e^{-10x}-10e^{-10x}x is 100e^{-10x}x-20e^{-10x}

What is the first derivative of e^{-10x}-10e^{-10x}x ?

The first derivative of e^{-10x}-10e^{-10x}x is 100e^{-10x}x-20e^{-10x}

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

100 e^{- 10 x} x - 20 e^{- 10 x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

- 10 e^{- 10 x} - 10 (- 10 e^{- 10 x} x + e^{- 10 x}) : 100 e^{- 10 x} x - 20 e^{- 10 x}

= 100 e^{- 10 x} x - 20 e^{- 10 x}

3 e^{x} cos (x)

\int \frac{3 x ^{2} + x + 3}{( x - 1 ) ^{3} ( x ^{2} + 1 )} d x

\int \frac{1}{( y - 1 ) ( y + 1 )} d y

\int \frac{1}{x \cdot ( ln ( x ) )} d x

x \to 1 lim (- x^{2} + 4 x - 8)

What is the derivative of e^{-10x}-10e^{-10x}x ?
The derivative of e^{-10x}-10e^{-10x}x is 100e^{-10x}x-20e^{-10x}
What is the first derivative of e^{-10x}-10e^{-10x}x ?
The first derivative of e^{-10x}-10e^{-10x}x is 100e^{-10x}x-20e^{-10x}