Basic Derivative Information and Power Rule
The derivative calculates the ________.
Slope
Define the Chain Rule for f(g(x))
g′(x)f′(g(x))
Define the Product Rule using f(x)g(x)
f′(x)g(x)+ g′(x)f(x)
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
d/dx (3x+1)²
6(3x+1)
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
d/dx sin(4x²)
8xcos(4x²)
y = x2∙cosx
y′ =-x2 sinx + 2x cosx
Differentiate y= tan(x)/x
y′= [x sec2(x)-tan(x)]/x2
Differentiate y=csc(x)
y′ =-csc(x)cot(x)
d/dx 3x²-x+3 =
6x-1
Differentiate y=√13x²-5x+8
y′ =26x-5/ 2√13x²-5x+8
Differentiate sin(x)cos(x)
y′ =cos2(x) - sin2(x)
f(x)= (x²-1)³/ x²+1, what is f′(x)?
f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²
d/dx sin(2x)
2cos(2x)
Perpendicular to tangent line
The normal line
Differentiate y=3tan√x
y′ =3sec²√(x)/ 2√x
Differentiate y=x²sin³(5x)
y′ =xsin²(5x)[15xcos(5x)+2sin(5x)]
Differentiate y= x2/(x+2) and find the slope at the point (2,1)
3/4
differentiate cos(x3)+(cos x)2
dy/dx=-3x2 sin(x3) - 2cos(x) sin(x)