Derivatives 4/28

Power Rule

100

d/dx(5x^3)

15x²

200

d/dx (6-3x)

-3

300

d/dx (1/8 x^4 - 3/4x^2)

1/2 x^3-3/2x

400

d/dx (2e+3π)

0

500

d/dx (x/3-x^2/3-x^3/3)

1/3 - 2/3x-x^2

rewrite power rule

100

d/dx(4/x^3)

-12/x^4

200

d/dx (14 sqrt(x))

7/sqrt(x) or 7/x^(1/2)

300

d/dx (1/x^(5/3))

-5/(3 x ^(8/3))

400

d/dx(10/sqrt(x))

-5/sqrt(x^3) or -5/x^(3/2

500

d/dx(6/x^2-3/x^(1/3))

-12/x^3+1/x^(4/3)

trigonometry

100

d/dx(sin(π/2x)

π/2cos(π/2x)

200

d/dx (4cos(3x))

-12sin (3x)

300

d/dx (tan(6x^2))

12x sec ² (6x² )

400

d/dx (cos(x^3)/3)

- x² sin (x³  )

500

d/dx (sin sqrt(x))

cos sqrt(x)/(2sqrt(x))

Exp and Log

100

d/dx (1/2e^(6x))

3 e ^6x

200

d/dx(ln(12x))

1/x

300

d/dx(e^sinx)

cosx * e^sinx

400

d/dx (10/e^(5x))

-50/e^(5x

500

d/dx (ln (2e^x))

1

tangent line

100

What is the slope of the line tangent to f(x) = x²   at x=4

m = 8

200

What is the slope of the line tangent to f(x) = cos x at x=  π/4 

m = -sqrt(2)/2

300

What is the equation of the line tangent to y = x² + 5x at x = 3

y - 24 = 11 ( x - 3)

400

What is the equation of the line tangent to f(x) = 2/x at x = 1/4 

y - 8 = -32 (x - 1/4)

500

What is the equation of the line tangent to f(x)= 4e^x at x = 0 ?

y - 4 = 4x  or y = 4x + 4