What is the derivative of (e^xdx) ?

The derivative of (e^xdx) is d(e^xx+e^x)

What is the first derivative of (e^xdx) ?

The first derivative of (e^xdx) is d(e^xx+e^x)

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

d (e^{x} x + e^{x})

Solution steps

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = x

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

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

\frac{d x}{d x} = 1

= d (e^{x} x + 1 \cdot e^{x})

Simplify

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

\frac{d}{d t} (sin (9 t))

x \to - \infty lim (2 x + 1)

x \to 3 + lim (\frac{2}{( x - 3 )})

x \to 1 + lim (2 - x^{2})

\int \frac{1}{7 - 5 x} d x

What is the derivative of (e^xdx) ?
The derivative of (e^xdx) is d(e^xx+e^x)
What is the first derivative of (e^xdx) ?
The first derivative of (e^xdx) is d(e^xx+e^x)