Basic Derivative Information and Power Rule
Product Rule
Quotient Rule
Trig Derivatives
Miscellaneous
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
At what values of a and b is f(x) differentiable.
a = -8
b = -5
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
Where is the function continuous but not differentiable.
x= -4 and x = 0
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
Find the equation of the tangent line of
y = x^4, x = -2
y - 16 = 32(x+2)
400
d/dx 3x²-x+3 =
6x-1
400
Differentiate y=e^-x²cos2x
y′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x
400
f(x)= tanx / x²+1, what is f′(x)?
f′(x)= [x2sec2x+sec2x - tan2x] / (x²+1)²
400
d/dx cot
-csc^2x
400
a(t) = 4h(t)f(t)
Find a'(1)
72
500
Speed is _________.
the absolute value of velocity
500
Differentiate y=x²secx
y′ = 2xsecx + x2secxtanx
500
Differentiate y= (x³lnx)/(x+2)
y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²
500
d/dx sec(x)=
secxtanx
500
h(x) = g(x)/2f(x) Find h'(-3).
-1/2