Unit 6 Review Introductory Calc

Trig. Derivatives

100

Find the first derivative of..

f(x)=sin(x)

f'(x)= cos(x)

200

Find the first derivative of..

y=cot(4x)

y'= -4csc²(4x)

300

Find the first derivative of..

y=4tan(x² +4)

y' = 8xsec²(x²+4)

400

Find the first derivative of..

y=x³cos(5x)

y' = 3x²cos(5x)-5x³sin(5x)

500

Find the first derivative of..

y=tan(x)sin(x)

y'  = sec²(x)sin(x)+tan(x)cos(x)

Trig 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= ln[ x²(2x³-2x)²]

y' = 2/x  + (6x²-2)/(x³-x)

Derivatives

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

Find the first derivative of..

y=e⁴ln(2x⁵)

y' = 5e⁴ / x

500

Find the first derivative of..

y=-e^-4x / ln(2x)

y' = [4xln(2x)+1] / [xe^4xln(2x)²]

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= ln(e^x)

y' = 1