What is the derivative of this function y=tan1(2x4)?

1 Answer
May 30, 2017

8x34x8+1

Explanation:

Aside from just applying the chain rule, one helpful way to perform this derivation may be to substitute a variable u to break the equation into separate pieces of a puzzle, like this:

We know the chain rule is
df(u)dx=dfdxdudx

We can also let u (in this case) = 2x4

Now just take the derivative of the function in two puzzle pieces:

We know ddu tan1(u) is just ddx(tan1(x))=1x2+1

SO...

ddu(tan1(u))=1u2+1

and

ddx(2x4)=8x3 (By the power rule)

From here, just substitute back u=2x4 to get 1(2x4)2+18x3

Which simplifies to... 8x34x8+1

V'oila! Our puzzle is complete!