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Popular >

derivative of ln^2(2*2^x-1/(x^2))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

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

Simplify

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

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Frequently Asked Questions (FAQ)

What is the derivative of ln^2(2*2^x-1/(x^2)) ?
The derivative of ln^2(2*2^x-1/(x^2)) is ln^3(2)*2^x+2/(x^3)
What is the first derivative of ln^2(2*2^x-1/(x^2)) ?
The first derivative of ln^2(2*2^x-1/(x^2)) is ln^3(2)*2^x+2/(x^3)