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})

h \to 0 lim (h sin (\frac{1}{h}))

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f (x) = x^{3} - x + 1, at x = 3

\int_{1}^{7} \frac{2}{x ^{3}} d 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)