What is the derivative of e^x(x^3-3x^2+6x-6) ?

The derivative of e^x(x^3-3x^2+6x-6) is e^xx^3

What is the first derivative of e^x(x^3-3x^2+6x-6) ?

The first derivative of e^x(x^3-3x^2+6x-6) is e^xx^3

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derivative of

e^{x} (x^{3} - 3 x^{2} + 6 x - 6)

e^{x} x^{3}

Solution steps

\frac{d}{d x} (e^{x} (x^{3} - 3 x^{2} + 6 x - 6))

Apply the Product Rule:

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

f = e^{x}, g = x^{3} - 3 x^{2} + 6 x - 6

= \frac{d}{d x} (e^{x}) (x^{3} - 3 x^{2} + 6 x - 6) + \frac{d}{d x} (x^{3} - 3 x^{2} + 6 x - 6) e^{x}

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

\frac{d}{d x} (x^{3} - 3 x^{2} + 6 x - 6) = 3 x^{2} - 6 x + 6

= e^{x} (x^{3} - 3 x^{2} + 6 x - 6) + (3 x^{2} - 6 x + 6) e^{x}

Simplify

e^{x} (x^{3} - 3 x^{2} + 6 x - 6) + (3 x^{2} - 6 x + 6) e^{x} : e^{x} x^{3}

= e^{x} x^{3}

\frac{\partial}{\partial z} (\frac{x - z}{y + z})

cos (x) \frac{π}{4}

x \to \infty lim (tan (x))

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

y^{^{''}} = 13 (y^{^{'}})^{2}

What is the derivative of e^x(x^3-3x^2+6x-6) ?
The derivative of e^x(x^3-3x^2+6x-6) is e^xx^3
What is the first derivative of e^x(x^3-3x^2+6x-6) ?
The first derivative of e^x(x^3-3x^2+6x-6) is e^xx^3