You are "Deriving" me crazy
f'(x)=2
This is the number of points that a tangent line touches a curve
What is "1"
This is the formula for the slope of a line given two points (x1,y1) and (x2,y2)
What is (y2−y1)/(x2−x1)
This rule allows you to find the derivative of the sum or difference of two functions by taking the derivative of each part separately.
What is the sum rule
This is what the limx->0f(x) equals if limx->0+ f(x)=1 and limx->0- f(x)=2
This is the derivative of f(x)=x147
f'(x)=147x146
This gives us both the derivative and the instantaneous rate of change.
The general form of this type of function is
P(x)=anxn+an−1xn−1+⋯+a2x2+a1x+a0
What is a polynomial function
This is the rule we use to differentiate a function of the form f(x)=xn
Where n is a real number
As x gets infinitesimally close to 2, f(x)= (x2-4)/(x2+x-6) goes to this number
what is 4/5
This is the derivative of f(x)=(3x+ex)(x3+5x+10)
f'(x)=(ex)(3x^2)+(e^x)(4+x^3)
What happens to the tangent line when a graph has a sharp corner.
What is not existing
This is the only point where a rational function of the form f(x)=g(x)/h(x) is undefined, where g and h are polynomial functions
What is h(x)=0
This is the rule we use to differentiate between two functions multiplied together.
As x gets infinitesimally close to 1, f(x)=(x-1)/(sqrt(x2+3)-2) goes to this number.
What is 2
This is the derivative of f(x)=(x2+3x+4)/(x2-1)
f'(x)=-(3x^2+10x+3)/(x^2-1)^2
When f(x) graphs a straight horizontal line, this is what happens to the slope of the tangent line
What is the slope of the tangent line being zero
This is the term for the point where the graph of a function intersects the x-axis.
What is a root or zero?
When f(x) graphs just a horizontal line, we would use this rule to find the derivative.
Constant Rule
As x gets infinitesimally close to infinity, f(x)=cos(x)/(x-1) goes to this number
What is 0
This is the derivative of f(x)=x4+7x2+e where we’ve substituted f into the limit definition of the derivative but haven’t solved it yet.
f'(x)=limh->0((x+h)4+7(x+h)2+e)-(x4+7x2+e)/h
The equation for the tangent line for the function
f(x)=2x3+x2+45 at the point (1,1)
What is y=8x-7
This is the quadratic formula used to solve a function of the form ax2+bx+c=0
x=−(b±sqrt(b2−4ac))/2a
This is the rule we use when we differentiate functions of the form f(x)=(g(x))/(h(x)) where g(x) and h(x) are functions
What is the Product rule
As x gets infinitesimally close to infinity, f(x)=(2x5/2-2x3/2+x)/(3x+x5/2-4) goes to this number
What is 2.