1. Differentiate each function and simplify as defected

a) y=2(x+2)⁴(4x-5)⁵ Simplify and write in factored form

2.simplify and completely. answers with radicals

f(x)=(6-3x+x⁴)^1/4

3.Given the function f(x)=4lnx+1/2x find equation of tangent line at x=1

4.Find the derivatives of each function

a) f(x)= 2e⁹+4logx-e^x

b) h(x)= -4x + lnx⁶ + log₄x

c) g(x)= -ex -2^x -x³

5.use implicit differentiation to find the slope of tangent line at given point

5e^x +10e^y =6 at point (0,0)

6use implicit differentiation to find dy/dx

10x + xy +2y⁵ =x⁹

7.find derivatives of each function and simplify

a) f(x)= ln(x⁴- 8x²)

b) y= x⁴e^5x

c) f(t) = e^6t+1

e^6t -1

8 suppose that for a company That make x stereos, cost and revenue equation are given by

c(x)= 75000+20 x R(x) = 175x - x²/12

where production output I 1 week is x stereo. If production is increasing at a rate of 575 stereo per week when production output is 7000 stereo, find the rate of increase or decrease in revenue and profit or dx/dt

a) find profit Function

b) rate increase revenue

c) rate increase profit

9.Givin the price demand equation x=f(p)=1215-5p²

a) find the elasticity of demand function

b) p= 18

c) p=5

d) p=9

9.A 15 foot ladder is place again wall. If the bottom of the ladder is pushed toward the wall at the rate of 0,7 foot per second, how fast is the top of ladder rising when the bottom of the ladder is 11 feet from wall

Vertical

H ?

15 feet

X =11 feet

Horizontal

a) list given information

b) write what you trying to find in leibniz notation

c) write general equation

d) find solutions