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!!!!!!!!!