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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

= A (\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})

= A (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}

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

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

f (x) = x^{\frac{1}{9}}

\frac{d}{d x} (8 - 5 x)

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

\int (2 x^{3} + x) (x^{4} + x^{2})^{108} d x

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