What is the derivative of e^{2x}(x-4(x+6)) ?

The derivative of e^{2x}(x-4(x+6)) is 2e^{2x}x^2+6e^{2x}x-46e^{2x}

What is the first derivative of e^{2x}(x-4(x+6)) ?

The first derivative of e^{2x}(x-4(x+6)) is 2e^{2x}x^2+6e^{2x}x-46e^{2x}

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\frac{d}{d x} (e^{2 x} (x - 4) (x + 6))

2 e^{2 x} x^{2} + 6 e^{2 x} x - 46 e^{2 x}

Solution steps

\frac{d}{d x} (e^{2 x} (x - 4) (x + 6))

Apply the Product Rule:

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

f = e^{2 x}, g = (x - 4) (x + 6)

= \frac{d}{d x} (e^{2 x}) (x - 4) (x + 6) + \frac{d}{d x} ((x - 4) (x + 6)) e^{2 x}

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

\frac{d}{d x} ((x - 4) (x + 6)) = 2 x + 2

= e^{2 x} \cdot 2 (x - 4) (x + 6) + (2 x + 2) e^{2 x}

Simplify

e^{2 x} \cdot 2 (x - 4) (x + 6) + (2 x + 2) e^{2 x} : 2 e^{2 x} x^{2} + 6 e^{2 x} x - 46 e^{2 x}

= 2 e^{2 x} x^{2} + 6 e^{2 x} x - 46 e^{2 x}

What is the derivative of e^{2x}(x-4(x+6)) ?
The derivative of e^{2x}(x-4(x+6)) is 2e^{2x}x^2+6e^{2x}x-46e^{2x}
What is the first derivative of e^{2x}(x-4(x+6)) ?
The first derivative of e^{2x}(x-4(x+6)) is 2e^{2x}x^2+6e^{2x}x-46e^{2x}