What is the derivative of 2x^3e^x(x^2-3x+1) ?

The derivative of 2x^3e^x(x^2-3x+1) is 2(e^xx^5+2e^xx^4-11e^xx^3+3e^xx^2)

What is the first derivative of 2x^3e^x(x^2-3x+1) ?

The first derivative of 2x^3e^x(x^2-3x+1) is 2(e^xx^5+2e^xx^4-11e^xx^3+3e^xx^2)

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

2 (e^{x} x^{5} + 2 e^{x} x^{4} - 11 e^{x} x^{3} + 3 e^{x} x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{3}, g = e^{x} (x^{2} - 3 x + 1)

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

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

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

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

Expand

3 x^{2} e^{x} (x^{2} - 3 x + 1) + (e^{x} x^{2} - e^{x} x - 2 e^{x}) x^{3} : e^{x} x^{5} + 2 e^{x} x^{4} - 11 e^{x} x^{3} + 3 e^{x} x^{2}

= 2 (e^{x} x^{5} + 2 e^{x} x^{4} - 11 e^{x} x^{3} + 3 e^{x} x^{2})

\int \frac{1}{y ^{2} 14 - y ^{2}} d y

\frac{2}{x}

6 \frac{d y}{d x} + 42 y = 7

\int_{1}^{4} (x + \frac{1}{x}) d x

y = x^{2} - \frac{1}{8} cos (x)

What is the derivative of 2x^3e^x(x^2-3x+1) ?
The derivative of 2x^3e^x(x^2-3x+1) is 2(e^xx^5+2e^xx^4-11e^xx^3+3e^xx^2)
What is the first derivative of 2x^3e^x(x^2-3x+1) ?
The first derivative of 2x^3e^x(x^2-3x+1) is 2(e^xx^5+2e^xx^4-11e^xx^3+3e^xx^2)