Reference no: EM13915012

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.