Chapter 4 Review- H. Calc

Trig. Derivatives

100

Find the first derivative of..

y=csc(x)

y'= -csc(x)cot(x)

200

Find the first derivative of..

y=cot(4x)

y'= -4csc²(4x)

300

Find the first derivative of..

y=4arcsin(x² +4)

y' = 4*(1/sqrt(1-(x²+4)²))*(2x)

400

Find the first derivative of..

y=arccos(x)

y' = -1/(sqrt(1-x²))

500

Find the first derivative of..

y=arctan(5x)

y'  = 5/(1+25x²)

Logarithmic Derivatives

100

Find the first derivative of..

y=ln(x)

y' = 1/x

200

Find the first derivative of..

y=ln(5x³-12x)

y' = (15x²-12) / (5x³-12x)

300

Find the first derivative of..

y=2x⁴ln(x) 

y' = 8x³ln(x) + 2x³

400

Find the first derivative of..

y=ln(x²-1)³

y' = 6x / (x²-1)

500

Find the first derivative of..

y= log₄(x²+4x)

y' = 1/((x²+4x)*ln(4))*(2x+4)

Misc.

100

Find the first derivative of..

y=e⁵

y'=0

200

Find the first derivative of..

y=e^-2x

y' = -2e^-2x

300

Find the first derivative of..

y=e^4xln(x)

y' = 4e^4xln(x) + (e^4x)/x

400

State the quotient rule

(LDH - HDL)/L^2

(u'v-uv')/v^2

500

Find the first derivative of..

y=-e^-4x / ln(2x)

y' = [4xln(2x)+1] / [xe^4xln(2x)²]

Exponential Derivatives

100

Find the first derivative of..

y= e^x

y'= e^x

200

Find the first derivative of..

y=4e^2x-2

y' = 8e^2x-2

300

Find the first derivative of..

y= e^-5x - e^x

y' = -5e^-5x - e^x

400

Find the first derivative of..

y=2x⁴e^-3x

y' = 8x³e^-3x - 6x⁴e^-3x

500

Find the first derivative of..

y= 4^(3x-2)

y' = 4^(3x-2)*ln(4)*(3)

Implicit Differentiation

100

Find the derivative of 

5x-y=6

y'=5

200

Find the derivative of 6xy=12

y'=x/y

300

Find the derivative of 

7xy-5y²+3x=5x

y'=(2-7y)/(7x-10y)

400

Find the values where there are vertical and horizontal tangents

5x-3y³+3y=4x²

HT: x=5/8

VT: y=+-sqrt(1/3)

To find points, plug the values into the original equation.

500

OTHER!! 

This is the name of Mr. Fishers dog. 

Who is Cindy Lou?