The Basics
The derivative of any constant value, such as f(x) = 7
0
"Low d-High, High d-Low," is used to remember this rule
Product Rule
This rule is required when finding the derivative of a composite function, like f(g(x))
Chain Rule
The derivative of sin(x)
cos(x)
This technique is used to find dy/dx when an explicitly mixes x and y variables and cannot be easily solved for y
Implicit Differentiation
What is the formula where to differentiate xn, you bring the exponent to the front to multiply, then reduce the exponent by one
Power rule
To find the derivative of f(x)/g(x) you use this rule
Quotient Rule
The derivative of (3x2+5)4 before simplifying
4(3x2+5)3 (6x)
The derivative of ln(x)
1/x
The derivative of arcsin(x)
1/sqrt 1-x2
The derivative of the natural exponential function ex
ex
The derivative of xex
ex(x+1)
The derivative of e5x
5e5x
This basic trig function has a derivative equal to sec2(x)
tan(x)
The slope of the tangent line to the curve x2 + y2 = 25 at the point (3,4)
-3/4
The derivative of 1/x3 expressed with a negative exponent
-3x-4
The derivative of x/(x+1)
1/((x+1)2)
The derivative of sqrt x2+1
x/sqrt x2+1
The derivative of cos(x2)
-2xsin(x2)
The derivative of arctan(x)
1/1+x2
The limit based formula used to define the derivative of any function F(X)
lim h->0 f(x+h) - f(x) / h
If h(x)=f(x)g(x)k(x), this is the expanded product rule formula for h'(x)
f'(x)g(x)k(x)+f(x)g'(x)k(x)+f(x)g(x)k'(x)
The derivative of cos3(x)
-3cos2(x)sin(x)
The derivative of the general exponential function f(x)= ax (where a>0)
axln(a)
If g(x) is the inverse function of f(x), this formula calculates g'(x) using the derivative of f
1/f'(g(x))