Find the equation of the tangent line at the indicated

Question

1. Find the derivation of the following functions. Show your work. Write which formula(s) you are using to aid you in receiving any partial credit.

a) f(x) = -9/x⁵ - 5√x⁴ + x⁷ - 4

b) g(x) = cos(2x) + e-2x -cot(x) - sec(x) + x +3

c) h(x) = cos(tan(x³))

d) f(x) = sin^-1(e^x)

e) g(x) = ln(x⁷ - 3x + 4)

f) h(x) = tan^-1(x) sin(x)

g) p(x) = e^x4-x8+1

h) f(x) = ln(5√(x²-9/x⁸))

i) g(x) =[e^xsec(5x)/x⁴-x^-1+8]

j) h(x) = sin(e^x sec^-1(x))

2. Given the following functions, find y''.

a) y = x-6/x+8

b) y = ln(sec(x))

3. Use implicit differentiation to find the indicated derivative.

a) x⁵ - y⁴ = 2xy, find dy/dx.

b) sec(θ)cos(r) = r³, find dθ/dr.

4. Find the equation of the tangent line at the indicated point.

a) f(x) = sin(x)sec(x) at x = π.

b) x² + y² = 169 at x = 5 with y < 0.