What is the derivative of 2^xln^2(x) ?

The derivative of 2^xln^2(x) is ln(2)*2^xln^2(x)+(2^{1+x}ln(x))/x

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

The first derivative of 2^xln^2(x) is ln(2)*2^xln^2(x)+(2^{1+x}ln(x))/x

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derivative

ln (2) \cdot 2^{x} ln^{2} (x) + \frac{2 ^{1 + x} ln ( x )}{x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2^{x}, g = ln^{2} (x)

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

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

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

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

\frac{2 ln ( x )}{x} \cdot 2^{x} = \frac{2 ^{1 + x} ln ( x )}{x}

= ln (2) \cdot 2^{x} ln^{2} (x) + \frac{2 ^{1 + x} ln ( x )}{x}

What is the derivative of 2^xln^2(x) ?
The derivative of 2^xln^2(x) is ln(2)*2^xln^2(x)+(2^{1+x}ln(x))/x
What is the first derivative of 2^xln^2(x) ?
The first derivative of 2^xln^2(x) is ln(2)*2^xln^2(x)+(2^{1+x}ln(x))/x