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

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

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

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

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

e^{x} x^{3} + 2 e^{x} x^{2} - 3 e^{x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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

\int_{- 1}^{1} (y^{2} - 2) - e^{y} d y

\frac{e ^{x^{2}} - 1}{x}

n \to \infty lim (- n^{2})

\frac{d}{d x} (2 x^{3} (1 - x^{2})^{4})

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