Could you help me better understand these Calculus concepts in steps?

Find the value ofdf^-1/dx at x = f(a).

f(x) = x³- 12x²- 4, x 8, a = 4

Use the table to determine the indicated derivative or state that the derivative cannot be determined.

x -16 -8 0 8 16

f(x) 4 5 6 7 8

f(x) 1 1/5 1/2 1/7 0

(f^-1)'(7)

Find the derivative.

g(x) = 6x²e^-x

Find an equation of the line tangent to the given curve at the point (a, f(a)).

f(x) = e^6x, a = 0

Find the value ofdf^-1/dx at x = f(a).

f(x) = 2x², x 0, a = 2

Find an equation of the line tangent to the given curve at the point (a, f(a)).

f(x) = -6e^5x, a = 0

Find the inverse of the function.

f(x) = (x - 6)², x 6

Use the table to determine the indicated derivative or state that the derivative cannot be determined.

x -4 -2 0 2 4

f(x) 2 3 4 5 6

f'(x) 1 1/5 1/2 1/7 0

(f(^-1)'f(-4))

Find the value ofdf^-1/dx at x = f(a).

f(x) = 5x + 10, a = 2

Evaluate the integral.

(e^2x - e^-2x) dx

Find the derivative.

f(x) = sin 3e^-3x