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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= 3 (e^{2 x} \cdot 2 + 2 (2 e^{2 x} x + e^{2 x}))

Expand

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

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

\int csc (2 x) cot (2 x) d x

\int_{0}^{π} sin (x) cos (n x) d x

t \frac{d y}{d t} + 3 y = 3 t

\frac{\partial}{\partial x} (4 x y + yz + 5 x z - 40)

\int - 5 e^{2 x} d x

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