midterm review Flashcards
Analytical definition of derivative?
Picture
What are the steps to finding a derivative?
- Rewrite radicals and make sure there are no variables in the denominator.
- Find the derivative
- No negative or fractional exponents
How to find equation of the line tangent to a function at a point?
Find the x, find the f(x), and find the f’(x). Then plug that into formula
What is the equation of a tangent line?
y - f(x) = f’(x) (x-x1) put pic
How to find equation of the line NORMAL or PERPENDICULAR to the tangent line?
Same formula, except find opposite reciprocal of your slope.
What are the rules of differentibility?
- Is continuous at x=c
2. The right and left hand DERIVATIVES are defined and equal at x=c
How can you tell whether a function is differentiable or not with a graph?
It has to be continuous at the point (no breaks) and it can’t have cusps(corner) or vertical tangents.
What is IROC? Formulas
Pic they’re the same thing, same formula for finding slope / derivative NC 11
Derivative of sin?
Cos
Derivative of cos(x)
-sin(x)
Derivative of tan(x)
Sec^2(x)
Derivative of cot(x)
-csc^2(x)
Derivative of sec(x)
Sec(x) tan(x)
Derivative of csc(x)
-csc(x) cot(x)
How do you find derivative of e?
Derivative of exponent times the original. Pic
