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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

x \to \frac{π}{2} lim (2 sec (x))

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

x \to 4 lim (x + 3)

\frac{d}{d x} (x d x)

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

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