What is the derivative of ln^2(2*2^x) ?

The derivative of ln^2(2*2^x) is ln^3(2)*2^x

What is the first derivative of ln^2(2*2^x) ?

The first derivative of ln^2(2*2^x) is ln^3(2)*2^x

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\frac{d}{d x} (ln^{2} (2) \cdot 2^{x})

ln^{3} (2) \cdot 2^{x}

Solution steps

\frac{d}{d x} (ln^{2} (2) \cdot 2^{x})

Take the constant out:

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

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

Apply the derivative exponent rule:

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

= ln^{2} (2) \cdot 2^{x} ln (2)

Simplify

ln^{2} (2) \cdot 2^{x} ln (2) : ln^{3} (2) \cdot 2^{x}

= ln^{3} (2) \cdot 2^{x}

What is the derivative of ln^2(2*2^x) ?
The derivative of ln^2(2*2^x) is ln^3(2)*2^x
What is the first derivative of ln^2(2*2^x) ?
The first derivative of ln^2(2*2^x) is ln^3(2)*2^x