What is (\partial)/(\partial x)(A(e^{2x}+2e^{2x}x)) ?

The answer to (\partial)/(\partial x)(A(e^{2x}+2e^{2x}x)) is A(4e^{2x}x+4e^{2x})

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(\partial)/(\partial x)(A(e^{2x}+2e^{2x}x))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial 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})

(x^{2} + y^{2})^{3} = 8 x^{2} y^{2}, (1, 1)

\frac{\partial}{\partial x} (x^{2} + y^{2} - z^{2})

\int_{- 2}^{- 1} \frac{4}{x ^{2}} d x

(13) (1 - 10)

3 e^{x}

What is (\partial)/(\partial x)(A(e^{2x}+2e^{2x}x)) ?
The answer to (\partial)/(\partial x)(A(e^{2x}+2e^{2x}x)) is A(4e^{2x}x+4e^{2x})