What is the derivative of e^{ax}a ?

The derivative of e^{ax}a is a^2e^{ax}

What is the first derivative of e^{ax}a ?

The first derivative of e^{ax}a is a^2e^{ax}

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

a^{2} e^{a x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= a e^{a x} a

Simplify

a e^{a x} a : a^{2} e^{a x}

= a^{2} e^{a x}

\frac{d y}{d x} = x^{3}

(x + y - 2) d x + (x - y + 4) d y = 0

\frac{\partial}{\partial x} (e^{x} + cos (x y))

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

\int \frac{2 x}{9 - x ^{4}} d x

What is the derivative of e^{ax}a ?
The derivative of e^{ax}a is a^2e^{ax}
What is the first derivative of e^{ax}a ?
The first derivative of e^{ax}a is a^2e^{ax}