What is the derivative of A(e^x+e^xx) ?

The derivative of A(e^x+e^xx) is A(e^xx+2e^x)

What is the first derivative of A(e^x+e^xx) ?

The first derivative of A(e^x+e^xx) is A(e^xx+2e^x)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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