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Math
Calculus
derivatives Calc 1
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Terms in this set (21)
The Derivative of Sin (x)
Cos (x)
The Derivative of Cos (x)
-Sin (x)
The Derivative of Tan (x)
Sec^2 (x)
The Derivative of csc (x)
-csc (x) Cot (x)
The Derivative of Sec (x)
Sec (x) Tan (x)
The Derivative of Cot (x)
-csc^2 (x)
The Derivative of -Sin (x)
-Cos (x)
The Derivative of Sqrt x
1/(2*Sqrt x)
The Chain Rule
The derivative of the outside times the derivative of the inside. ex: f'[g(x)] * g'(x)
The Quotient Rule
The denominator times the derivative of the numerator, minus the numerator times the derivative of the denominator all divided by the denominator squared. ex: [g(x)f'(x)-f(x)g'(x)]/(g(x))^2
what is The limit, as x approaches 0, of the sin of x divided by x?
lim (sin (x))/x
x->0
the limit is 1
what is The limit, as x approaches 0, of the cos of x minus 1 all divided by x?
lim (cos (x)-1)/x
x->0
The limit is 0
What is the limit, as x approaches infinity, of a function
a^2+or -..... all divided by b^2+or-....?
The function limits to the coefficients a/b
What is the limit, as x approaches infinity, of a function
a^2+or -..... all divided by b^3+or-....?
The function limits to 0 because the highest exponent in the denominator is greater than the highest exponent in the numerator.
What is the Derivative of ln(x)?
e^x
Any number, except for the number zero itself, raised to the zero power equals?
Any number, except for the number zero itself, raised to the zero power equals 1
Multiplying like bases will do what to the exponents?
Multiplying like bases will ADD the exponents together.
Raising a power to a power will do what to the exponents?
Raising a power to a power will multiply the exponents together.
What is the integral of Tan^2(x)?
Tan(x)-x
What is Rolles Theorem?
States: if f(x) is continuous and differentiable on the interval [a,b]; then within the interval lies a point, c, such that f'(c)=0
What is the mean value theorem?
States; if f(x) is continuous and differentiable on the interval [a,b]; then within the interval lies a point, c, such that f'(c)= f(b)-f(a)/b-a
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