Power Rules

Rewrite

100

f(x)=7/x³

f(x)=7x^-3

200

f(x) = 8/x⁸

f(x) = 8x^-8

300

f(x) = 5/x⁶ - 3/x³ + 2/x²

f(x) = 5x^-6 - 3x^-3 + 2x^-2

400

f(x) = 2x²/x - 9/x⁹

f(x) = 2x - 9x^-9

500

f(x) = 7/x^-4 - 2x³ + 2/x¹⁸

f(x) = 7x⁴ - 2x³ + 2x^-18

Tangent Line (Y=)

100

Find the equation of the tangent line at the point where x=1 for the function f(x)=x²-3x+5

y=-x+3

200

Find the equation of the tangent line at the point where x=0 for the function f(x)=3x³-2x²+x+4

y=1

300

Find the equation of the tangent line at the point where x=-2 for the function f(x)=4x-2

y=4x+10

400

Find the equation of the tangent line at the point where x=3 for the function f(x)=2x²+5x-1

y=17x-34

500

Find the equation of the tangent line at the point where x=4 for the function f(x)=x³-3x²+2x+1

y=26x-39

Normal Line (Y=)

100

Find the equation of the normal line to the function f(x)= x³-3x²+2x at x=1

y=x-1

200

Find the equation of the normal line to the function f(x)= x³-4x at x=1

Y=x-4

300

Find the equation of the normal line to the function f(x)= 3x^2-2x+1 at x=-1

y=(1/8)x + (49/8)

400

Find the equation of the normal line to the function f(x)= 1/x² at x=-2

y= -4x - 31/4

500

Find the equation of the normal line to the function f(x)= √x at x=4

y=-4x+18

Derivatives

100

f(x)=3x⁴−2x³+x²

f′(x)=12x³−6x²+2x

200

f(x)=10x⁵−x⁴+3x²

f′(x)=50x⁴−4x³+6x

300

f(x)=4x³−5x²+2x−7

F'(x) = 12x²-10x+2

400

f(x)=7x⁵−3x⁴+x³−2x

f′(x)=35x⁴−12x³+3x²−2

500

f(x)=−5x⁷+8x⁵−3x²

f′(x)=−35x⁶+40x⁴−6x