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

1 Answer

Aug 26, 2015

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

Explanation:

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})#

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