Help with differentiation C4

I'm doing a question in the C4 textbook which involves differentiating

2^{-x}

I tried to from first principles and got

\dfrac{-ln2}{2^x}

Is this the right answer? Do you always have to differentiate from first principles with questions like these?

Thank you!

Original post by Serpentine111

I'm doing a question in the C4 textbook which involves differentiating

2^{-x}

I tried to from first principles and got

\dfrac{-ln2}{2^x}

Is this the right answer? Do you always have to differentiate from first principles with questions like these?

Thank you!

That's right and no you certainly don't need first principles!

2^{-x}=e^{\ln 2^{-x}}=e^{-x \ln 2}

That's right and no you certainly don't need first principles!

2^{-x}=e^{\ln 2^{-x}}=e^{-x \ln 2}

Thank you! I never thought to do it like that :colondollar:

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