What is the derivative of se^{sx} ?

The derivative of se^{sx} is s^2e^{sx}

What is the first derivative of se^{sx} ?

The first derivative of se^{sx} is s^2e^{sx}

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

s^{2} e^{s x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (s x) = s

= s e^{s x} s

Simplify

s e^{s x} s : s^{2} e^{s x}

= s^{2} e^{s x}

What is the derivative of se^{sx} ?
The derivative of se^{sx} is s^2e^{sx}
What is the first derivative of se^{sx} ?
The first derivative of se^{sx} is s^2e^{sx}