What is the derivative of 3(4e^{2x}x+4e^{2x}) ?

The derivative of 3(4e^{2x}x+4e^{2x}) is 3(8e^{2x}x+12e^{2x})

What is the first derivative of 3(4e^{2x}x+4e^{2x}) ?

The first derivative of 3(4e^{2x}x+4e^{2x}) is 3(8e^{2x}x+12e^{2x})

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\frac{d}{d x} (3 (4 e^{2 x} x + 4 e^{2 x}))

3 (8 e^{2 x} x + 12 e^{2 x})

Solution steps

\frac{d}{d x} (3 (4 e^{2 x} x + 4 e^{2 x}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (4 e^{2 x} x + 4 e^{2 x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 3 (\frac{d}{d x} (4 e^{2 x} x) + \frac{d}{d x} (4 e^{2 x}))

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

\frac{d}{d x} (4 e^{2 x}) = 8 e^{2 x}

= 3 (4 (2 e^{2 x} x + e^{2 x}) + 8 e^{2 x})

Expand

4 (2 e^{2 x} x + e^{2 x}) + 8 e^{2 x} : 8 e^{2 x} x + 12 e^{2 x}

= 3 (8 e^{2 x} x + 12 e^{2 x})

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\frac{d y}{d x} = \frac{e ^{x}}{7 + e ^{x}}

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What is the derivative of 3(4e^{2x}x+4e^{2x}) ?
The derivative of 3(4e^{2x}x+4e^{2x}) is 3(8e^{2x}x+12e^{2x})
What is the first derivative of 3(4e^{2x}x+4e^{2x}) ?
The first derivative of 3(4e^{2x}x+4e^{2x}) is 3(8e^{2x}x+12e^{2x})