What is the derivative of $arctan(8^x)$ ?

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Answer 1 · 2015-08-26T21:57:21

$(ln(8)8^{x})/(1+8^{2x})$

Use the Chain Rule and the facts that $d/dx(arctan(x))=1/(1+x^2)$ and $d/dx(8^{x})=ln(8) * 8^{x}$ to get:

$d/dx(arctan(8^{x}))=1/(1+(8^{x})^2) * d/dx(8^{x})$

$=(ln(8)8^{x})/(1+8^{2x})$

What is the derivative of arctan(8^x)arctan(8^x)?