What is the derivative of y=(x^3-x)e^{-3}x ?

The derivative of y=(x^3-x)e^{-3}x is (4x^3-2x)/(e^3)

What is the first derivative of y=(x^3-x)e^{-3}x ?

The first derivative of y=(x^3-x)e^{-3}x is (4x^3-2x)/(e^3)

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derivative of

y = (x^{3} - x) e^{- 3} x

\frac{4 x ^{3} - 2 x}{e ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{3} - x, g = x

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

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

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

= e^{- 3} ((3 x^{2} - 1) x + 1 \cdot (x^{3} - x))

Simplify

e^{- 3} ((3 x^{2} - 1) x + 1 \cdot (x^{3} - x)) : \frac{4 x ^{3} - 2 x}{e ^{3}}

= \frac{4 x ^{3} - 2 x}{e ^{3}}

z (3 x)^{4}

\frac{x}{10}

lo g_{10} (3 x + 2016)

\frac{d}{d t} (10 t)

\frac{d}{d a} (4 a)

What is the derivative of y=(x^3-x)e^{-3}x ?
The derivative of y=(x^3-x)e^{-3}x is (4x^3-2x)/(e^3)
What is the first derivative of y=(x^3-x)e^{-3}x ?
The first derivative of y=(x^3-x)e^{-3}x is (4x^3-2x)/(e^3)