Rules
the derivative of a constant function
What is 0?
the derivative of f(x)=x2
What is 2x
What is the formula for the slope of the tangent line at a point?
y-y1 = m(x-x1)
sin(3x2)
Find d/dx
6xcos(3x2)
Define implicit differentiation
Implicit differentiation is a method for finding the derivative of a function that cannot be expressed explicitly in the form y = f(x)
Used when we are differentiating with respect to x but have a y in 1 or more terms
the Power Rule for differentiation
What is nx^(n-1)?
Calculate the derivative of f(x)=3x^3 + 5x
What is 9x^2 + 5
Find the equation of the tangent line to f(x)=x2 at the point x=1
y-1 =2(x-1)
5sec2(5x + 2)
Find d/dx
cos(x3−4x)
Find dy/dx
x2+y2=25
dy/dx = -x/y
the derivative of a product of two functions
What is U'V+V'U?
the derivative of f(x)=ln(x)
What is 1/x?
How do you find the normal line to the curve at a given point?
The slope is the opposite reciprocal
csc(4x2)
−8xcsc(4x2)cot(4x2)
Find dy/dx is x3+y3=6xy
Do not Simplify
(3x2+6y)/(-3y2+6x)= dy/dx
dy/dx
What is differentiating a term with a Y?
the derivative of f(x)=sec(x)
What is Sec(x)Tan(x)?
Calculate the slope of the tangent to the curve f(x)=ln(x) at x=e
y-1= 1(x-e)
y=sec(2x+3)
dx/dy = 2sec(2x+3)tan(2x+3)
Find dy/dx
x2y+y2=3x
(3-2xy)/(x2+2y)= dy/dx
Explain the chain rule
What is the derivative of the outside function with respect to the inside function times the derivative of the inside function?
The 6 Main Trig functions and their derivatives
What is
d/dx[sin x] = cos x
d/dx[cos x] = - sin x
d/dx[tan x] = sec ^2 x
d/dx[Cot x] = -csc ^2
d/dx[csc x] = - csc x cot x
d/dx[sec x]= sec x tan x
If the tangent line to the curve f(x)=x3 at x=2 is required, find its equation
y-8 = 12(x-2)
Differentiate:
(sin(3x2+2)(tan(x))/(x2+1)
6xcos(3x2+2)tanx + sin(3x2+2)(sec2(x)(x2+1)-2xsin(3x2+2)tan(x)/(x2+1)2
Explain Implicit Differentiation using transferable steps of thinking
Answers may Vary ...
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