What is the derivative of a(e^x+e^{xx}) ?

The derivative of a(e^x+e^{xx}) is a(e^x+e^{x^2}*2x)

What is the first derivative of a(e^x+e^{xx}) ?

The first derivative of a(e^x+e^{xx}) is a(e^x+e^{x^2}*2x)

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\frac{d}{d x} (a (e^{x} + e^{xx}))

a (e^{x} + e^{x^{2}} \cdot 2 x)

Solution steps

\frac{d}{d x} (a (e^{x} + e^{xx}))

Simplify

a (e^{x} + e^{xx}) : a (e^{x} + e^{x^{2}})

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

f (x) = \frac{1}{x + 1}

x \to \infty lim (y^{- x})

x \to 2 lim (5)

e^{- x}, 0, 0, ln (3)

\frac{d y}{d t} = 6 y + 2 t - 4, y (0) = 3

What is the derivative of a(e^x+e^{xx}) ?
The derivative of a(e^x+e^{xx}) is a(e^x+e^{x^2}*2x)
What is the first derivative of a(e^x+e^{xx}) ?
The first derivative of a(e^x+e^{xx}) is a(e^x+e^{x^2}*2x)