What is the derivative of f(x)=3a^{3x} ?

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

What is the first derivative of f(x)=3a^{3x} ?

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

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derivative of

f (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)

9 x^{2} + y = 9, x^{4} - y = 1

\int \frac{3}{y} d y

x \to 1 lim (\frac{- 3 x - 1}{x - 1})

\int (e^{x} + 2)^{2} e^{x} d x

2 sin (3 θ), 1

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