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

The derivative of 3a^{3x} is 9a^{3x}ln(a)

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

The first derivative of 3a^{3x} is 9a^{3x}ln(a)

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

9 a^{3 x} ln (a)

Solution steps

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

Take the constant out:

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

= 3 \frac{d}{d x} (a^{3 x})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

3 e^{3 x l n (a)} \cdot 3 ln (a) : 9 a^{3 x} ln (a)

= 9 a^{3 x} ln (a)

y = sin^{5} (3 x)

\int 2 x + 3 d x

\frac{d}{d x} (5 - 6 x)

\int x (x + 3) d x

\frac{d}{d x} (3 x^{2} - 27)

What is the derivative of 3a^{3x} ?
The derivative of 3a^{3x} is 9a^{3x}ln(a)
What is the first derivative of 3a^{3x} ?
The first derivative of 3a^{3x} is 9a^{3x}ln(a)