you should know the chain rule and how to derive a fraction of functions or multiples of functions
if
the second one you need to make a trick let
take the ln
derive both sides
show some work
Differentiate the following functions and simplify:
a) (x^4+2x^1/2)(lnx)
b) x^(x^2)
c) sinx/x^6
d) (e^4x^2)-2.
N:B The parentheses is not in the question, I only used it to separate -2 from x as it is not part of the power of x and to make the question clearer
2) Determine the derivative of the inverse f^-1 of f(x) =3^(x/2)+logx(base 2)+(x^3) -7 at the point 5=f(2).
Write down the equation of the tangent line of f^-1 at 5.
Thanks in advance.
Happy New Year!!!!!!!!!
in a) i already solved with chain rule
here is what i did.
(x^4+2x^1/2)(lnx)
4x^3+x^(-1/2)*lnx + (x^4+2x^1/2)*1/x
how can i simplify this?
b) here's what i did as you have said
y=x^(x^2)
lny=ln x^(x^2)
1/y=x^2lnx
using chain rule,
1/y= x^2*1/x+2x*lnx
1/y=x+2xlnx
1/y=x(1+2lnx)
it doesn't seem right to me, i think i have missed something.
i need help!
Take a look here:
Inverse function theorem - Wikipedia, the free encyclopedia