Basic Derivative Information and Power Rule
The derivative calculates the ________.
Slope
Define the Quotient Rule using f(x)/g(x)
[g(x)f′(x) - f(x)g′(x)]/ (g(x))²
d/dx cosx=
-sinx
d/dx 5 =
0
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
Differentiate y= 2/(x+1)
y′ = -2/ (x+1)²
Differentiate y=tan(x)
y′ =sec²(x)
d/dx x² =
2x
Differentiate y=x³(x+1)
y′ =4x3+3x2
Differentiate y= (1+x) / (x²-x)
y′= (-x2-2x+1)/(x2-x)2
Differentiate y=csc(x)
y′ =-csc(x)cot(x)
d/dx 3x²-x+3 =
6x-1
Differentiate y=-x²cosx
y′ =x2sinx-2xcosx
f(x)= (x²-1)2/ x²+1, what is f′(x)?
f′(x)=(2x5+4x3-6x)/(x2+1)2
d/dx secx
secxtanx
Speed is _________.
the absolute value of velocity
Differentiate y=x²sinx-2x3cosx
y′ =2xsinx+x2cosx-6x2cosx+2x3sinx
Differentiate y= (x³sinx)/(x+2)
y′ = [x2(2xsinx+6sinx+x2cosx+2xcosx)]/(x+2)2
d/dx cotx/cscx
-csc2x-cot2x/cscx