Derivatives

Basic Rules

100

Find the first Derivative of: f(x)=2x²-16x+35

4x-16

200

  Find the derivative of: R(z)=(5z-8)^1/2

R'(z)= 5/(2*(5z-8)^1/2)

300

Find the derivative of y' if y'=((2^1/2)x-3)/6

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

400

Find the derivative of y=2(x^1/2)-1/(2(x^1/2))

(4x-1)/(4x(x^1/2))

500

 Find the slope of the line tangent to f(x)=5x⁶+2x⁵+3x⁴+9x³+3x²+6x+23 at x=0

6 

since f'(x)= 30x⁵+10x⁴+12x³+27x²+6x+6

and f'(0)= 6

Trigs

100

Find the derivative of f(x)=sin(tan x)

sec²x cos(tan x)

200

Find the derivative of sin^-1(2x)

2/(1-4x²)^(1/2)

300

Find the derivative of [cos(x)sin(x)tan(x)]

sec(x)sin(x)+cos²(x)tan(x)-sin²(x)tan(x)

400

Find the second derivative of arcsin(2x)

(8x)/(1-4x²)^(3/2)

500

Find dy/dx if x= sin(t²) and y=cos(t²)

-tan(t²)

Exponentials

100

Find the derivative of 2^x

(2^x)*(ln2)

200

Find f’(x) when f(x)=2^{ln x}

(2^{ln x})*(ln 2)/x

300

Find the derivative of f(x)= ln(1/x)

x

400

Find the derivative of f(x)=ln (sin x)

cotx

500

Find the derivative of 10^x(23x²+23x+23)

ln(10)(23x²+23x+23)(10^x)+(46x+23)(10^x)

Implicits

100

Find y' for 2xy-3x²+5x²y+6y²=0

y'=(6x-10xy-2y)/(2x+12y+5x²)

200

Find the differential equation of 5x²y+y=25

dy/dx=-(10xy)/5x²+1)

300

Find dy/dx for 3x²y²-2y²+7y³=100x

dy/dx=(100-6xy²)/(6x²y-4y+21y²)

400

Find d²y/dt² when y=sin(x) and x=cos(x) in simplified form

d²y/dt²=(csc x)³

500

Find d²y/dx² when dy/dt=3x²+x and dx/dt=x in simplified form

d²y/dx²=3/x