What is the derivative of 2(16e^{4x}x+8e^{4x}) ?

The derivative of 2(16e^{4x}x+8e^{4x}) is 2(64e^{4x}x+48e^{4x})

What is the first derivative of 2(16e^{4x}x+8e^{4x}) ?

The first derivative of 2(16e^{4x}x+8e^{4x}) is 2(64e^{4x}x+48e^{4x})

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\frac{d}{d x} (2 (16 e^{4 x} x + 8 e^{4 x}))

2 (64 e^{4 x} x + 48 e^{4 x})

Solution steps

\frac{d}{d x} (2 (16 e^{4 x} x + 8 e^{4 x}))

Take the constant out:

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

= 2 \frac{d}{d x} (16 e^{4 x} x + 8 e^{4 x})

Apply the Sum/Difference Rule:

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

= 2 (\frac{d}{d x} (16 e^{4 x} x) + \frac{d}{d x} (8 e^{4 x}))

\frac{d}{d x} (16 e^{4 x} x) = 16 (4 e^{4 x} x + e^{4 x})

\frac{d}{d x} (8 e^{4 x}) = 32 e^{4 x}

= 2 (16 (4 e^{4 x} x + e^{4 x}) + 32 e^{4 x})

Expand

16 (4 e^{4 x} x + e^{4 x}) + 32 e^{4 x} : 64 e^{4 x} x + 48 e^{4 x}

= 2 (64 e^{4 x} x + 48 e^{4 x})

What is the derivative of 2(16e^{4x}x+8e^{4x}) ?
The derivative of 2(16e^{4x}x+8e^{4x}) is 2(64e^{4x}x+48e^{4x})
What is the first derivative of 2(16e^{4x}x+8e^{4x}) ?
The first derivative of 2(16e^{4x}x+8e^{4x}) is 2(64e^{4x}x+48e^{4x})