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Popular Calculus >

derivative of (x-1e^{x^2-4})

Solution

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

Solution

e^{x^{2} - 4} + 2 e^{x^{2} - 4} x (x - 1)

Solution steps

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

Apply the Product Rule:

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

f = x - 1, g = e^{x^{2} - 4}

= \frac{d}{d x} (x - 1) e^{x^{2} - 4} + \frac{d}{d x} (e^{x^{2} - 4}) (x - 1)

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

\frac{d}{d x} (e^{x^{2} - 4}) = e^{x^{2} - 4} \cdot 2 x

= 1 \cdot e^{x^{2} - 4} + e^{x^{2} - 4} \cdot 2 x (x - 1)

Simplify

= e^{x^{2} - 4} + 2 e^{x^{2} - 4} x (x - 1)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x-1e^{x^2-4}) ?
The derivative of (x-1e^{x^2-4}) is e^{x^2-4}+2e^{x^2-4}x(x-1)
What is the first derivative of (x-1e^{x^2-4}) ?
The first derivative of (x-1e^{x^2-4}) is e^{x^2-4}+2e^{x^2-4}x(x-1)