What is the derivative of (e^{2x}dx) ?

The derivative of (e^{2x}dx) is d(2e^{2x}x+e^{2x})

What is the first derivative of (e^{2x}dx) ?

The first derivative of (e^{2x}dx) is d(2e^{2x}x+e^{2x})

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

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

Solution steps

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = e^{2 x}, g = x

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

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

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

= d (e^{2 x} \cdot 2 x + 1 \cdot e^{2 x})

Simplify

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

\int (x^{3} e^{x^{4}}) d x

t^{2} \frac{d y}{d t} + y = 0

(tan^{c o s (x)} (x))^{^{'}}

y = (1 + 5 x)^{10}

\frac{d}{d x} (- x + \frac{1}{x} + 1)

What is the derivative of (e^{2x}dx) ?
The derivative of (e^{2x}dx) is d(2e^{2x}x+e^{2x})
What is the first derivative of (e^{2x}dx) ?
The first derivative of (e^{2x}dx) is d(2e^{2x}x+e^{2x})