Basic Derivative Information and Power Rule
Product Rule
Quotient Rule
Trig Derivatives
Random Derivatives
100
The derivative calculates the ________.
Slope
100
Define the Product Rule using f(x)g(x)
f′(x)g(x)+ g′(x)f(x)
100
Define the Quotient Rule using f(x)/g(x)
[g(x)f′(x) - f(x)g′(x)]/ (g(x))²
100
d/dx cosx=
-sinx
100

d/dx(3\sqrt(h))

(3/2)h^(-1/2)

200
d/dx 5 =
0
200
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
200
Differentiate y= 2/(x+1)
y′ = -2/ (x+1)²
200
Differentiate y=tan(x)
y′ =sec²(x)
200

d/dx ( 4x^-2 + 5x^2 +10)

-8x^-3 + 10x

300
d/dx x² =
2x
300
Differentiate y=x³lnx
y′ =x²(1+3lnx)
300
Differentiate y= (1+lnx) / (x²-lnx)
y′= [(1/x)-x-2xlnx] / (x²-lnx)²
300
Differentiate y=csc(x)
y′ =-csc(x)cot(x)
300

d/dx ( \sqrt(x) + 1/(\sqrt(x) ) 

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


1/(2\sqrt(x)) - 1/(2\sqrt(x^3))

400
d/dx 3x²-x+3 =
6x-1
400
Differentiate y=e^-x²cos2x
y′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x
400
f(x)= (x²-1)³/ x²+1, what is f′(x)?
f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²
400

d/dx sin(x)

cos(x)

400

d/dx ( 1/2 x^4/5 - 3/x^(5) ) 

2/5x^(1/5) + 15/x^(6)

500

The derivative of position is...?

Velocity

500
Differentiate y=x²sin³(5x)
y′ =xsin²(5x)[15xcos(5x)+2sin(5x)]
500
Differentiate y= (x³lnx)/(x+2)
y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²
500
d/dx arcsec(x)=
1/ |x| √(x² - 1)
500

d/dx ( 5x * \sqrt(x)

(5x)/(2x^1/2) + 5\sqrt(x)

M
e
n
u