What is the derivative of a^{2x+3} ?

The derivative of a^{2x+3} is 2a^{2x+3}ln(a)

What is the first derivative of a^{2x+3} ?

The first derivative of a^{2x+3} is 2a^{2x+3}ln(a)

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derivative of

a^{2 x + 3}

2 a^{2 x + 3} ln (a)

Solution steps

\frac{d}{d x} (a^{2 x + 3})

Apply exponent rule:

a^{b} = e^{b l n (a)}

a^{2 x + 3} = e^{(2 x + 3) l n (a)}

= \frac{d}{d x} (e^{(2 x + 3) l n (a)})

Apply the chain rule:

e^{(2 x + 3) l n (a)} \frac{d}{d x} ((2 x + 3) ln (a))

= e^{(2 x + 3) l n (a)} \frac{d}{d x} ((2 x + 3) ln (a))

\frac{d}{d x} ((2 x + 3) ln (a)) = 2 ln (a)

= e^{(2 x + 3) l n (a)} \cdot 2 ln (a)

e^{(2 x + 3) l n (a)} = a^{2 x + 3}

= 2 a^{2 x + 3} ln (a)

What is the derivative of a^{2x+3} ?
The derivative of a^{2x+3} is 2a^{2x+3}ln(a)
What is the first derivative of a^{2x+3} ?
The first derivative of a^{2x+3} is 2a^{2x+3}ln(a)