What is the derivative of (e^tx+1)dx ?

The derivative of (e^tx+1)dx is e^txdx

What is the first derivative of (e^tx+1)dx ?

The first derivative of (e^tx+1)dx is e^txdx

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derivative of

(e^{t} x + 1) d x

e^{t} x d x

Solution steps

\frac{d}{d t} ((e^{t} x + 1) d x)

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d t} (1) = 0

= d x (x e^{t} + 0)

Simplify

= e^{t} x d x

\frac{\partial}{\partial x} (2 y + x)

\int y - y d y

\frac{13}{ln ( x )}

y = \frac{1}{x}, at x = 4

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

What is the derivative of (e^tx+1)dx ?
The derivative of (e^tx+1)dx is e^txdx
What is the first derivative of (e^tx+1)dx ?
The first derivative of (e^tx+1)dx is e^txdx