What is the derivative of f(x)=a^{2x} ?

The derivative of f(x)=a^{2x} is 2a^{2x}ln(a)

What is the first derivative of f(x)=a^{2x} ?

The first derivative of f(x)=a^{2x} is 2a^{2x}ln(a)

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derivative of

f (x) = a^{2 x}

2 a^{2 x} ln (a)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

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