Derivatives, Derivatives & More Derivatives

Basic

100

y=3x+4x^-3

y'=3-12x^-4

200

f(x)=3sqrtx-1/x^7

f'(x)=3/2x^(-1/2)+7x^-8

300

y=4x^(-2/8)-x^3

y'=-x^(-10/8)-3x^2

400

y=1/sqrt(x^5)

y'=-5/2x^(-7/2)

500

g(x)=-3lnx-5/(root(4)(x^3))+2

g'(x)=-3/x-15/4x^(-7/4)

Trig

100

sinx-7cosx

y'=cosx+7sinx

200

y=-10tanx

y'=-10sec^2x

300

y=sinx+3x^4cosx

y'=cosx+(12x^3cosx-cosx(3x^4))

400

y=-2cotx+tanx+sinxcosx

y'=2cotxcscx+sec^2x+(cosxcosx-sinxsinx)

500

y=cotx/tanx

y'=(-cotxcscxtanx-sec^2xcotx)/tan^2x

Mix

100

y=x^2+4sqrtx

y'=2x+4(1/2)x^(-1/2) 

200

y=(2-x)/(3x+4)

y'=((3x+4)(-1)-(2-x)(3))/(3x+4)^2

300

y= x^4 (x^3+3x-1)

y'=4x^3(x^3+3x-1)+(3x^2+3)(x^4)

400

y=(-x^3+lnx-x)(e^x-cosx)

y'=(-3x^2+1/x-1)(e^x-cosx)+(e^x+sinx)(-x^3+lnx-x)

500

y=(lnx)/sinx+4x^-2

y'=((1/x(sinx)-cosxlnx)/sin^2x)-8x^-3

Extra

100

Find the slope of f(x) when x=1

f(x)=x^3+2x^2+5

7

200

Write the equation of the tangent line at x=pi for

f(x)=(e^x+5)sinx

f'(x)=e^xsinx+cosxe^x

f'(4)=-e^pi

f(pi)=0

y-0=-e^pi(x-pi)

300

Find the instantaneous rate of change of the function at x = 1.

f(x)=sinxsecx

f'(x)=cosxsecx+secxtanxsinx

f'(1)=1

400

Find the x-value(s) where the tangent to the graph is parallel to the x-axis.

f(x)=3x^4-5x^3+2

x=0, 5/4

500

Find the equation of the tangent at (0, 1) of the curve,

y=3x+5cosx

y'=3-5sinx

y'(0)=3

y-1=3(x-0)