Derivatives (Name the function who's derivative is shown!)
The average rate of change of a function from (a, b) is represented by
f'(c)=(f(b)-f(a))/(b-a)
What is the Mean Value Theorem for derivative?
For
d/dx fg=fg'+gf'
What is the Derivative product rule?
d/dx (5)
What is 0?
For a continuous function from [a,b], if f(a)<0 and f(b)>0 then there exists at least one number c in the interval (a,b) such that f(c)=0.
What is Intermediate Value Theorem (IVT)?
For f(g(x))
f'(g(x))g'(x)
What is the Derivative chain rule?
int(5)dx
He was credited for defining and evaluating e?
Who is Leonhard Euler?
secx tanx
What is the derivative of secx?
For a continue function f from [a,b], such that F is an antiderivative of f;
int_a^b f dx=F(b)-F(a)
What is the Fundamental Theorem of Calculus?
For
y=x^n , y'=nx^(n-1)
What is derivative power rule?
d/dx sqrtx
What is
1/2 x^(-1/2
He is credited for the Fundamental Theorem of Algebra.
Who is Karl Gauss?
sec^2x
What is the derivative of tanx?
lim_(Deltax->0) (f(x+Deltax)-f(x))/(Deltax)
What is The derivative of f(x) or limit definition of derivative?
d/dx f/g=(gf'-fg')/g^2
What is the Derivative quotient rule?
lim_(x->3) 5/(x-3)
What is DNE?
Best known for his contributions in mathematics, astronomy, and music. He is named for a theorem that relates the sides of a right triangle.
Who is Pythagoras?
-csc^2x
What is the derivative of cotx?
f(c)=1/(b-a)int_a^b(f(x))dx
What is The Average Value of a Function (or MVT for Integration)?
int(x^n)dx=x^(n+1)/(n+1)+c
int_-1^1 (x)dx
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