What is the derivative of ae^{bx} ?

The derivative of ae^{bx} is ae^{bx}b

What is the first derivative of ae^{bx} ?

The first derivative of ae^{bx} is ae^{bx}b

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

a e^{b x} b

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= a e^{b x} b

x \to 2 lim (2 x)

\int \frac{100}{7 x - 16} d x

\frac{d}{d x} (\frac{4}{x + 2 x})

f (x) = 3 x^{\frac{2}{3}}

\frac{4 x ^{2} + 6 x + 2}{x}

What is the derivative of ae^{bx} ?
The derivative of ae^{bx} is ae^{bx}b
What is the first derivative of ae^{bx} ?
The first derivative of ae^{bx} is ae^{bx}b