Show:
Derivatives
Formulas
Rules
Whats the U?
History
100
cosx
What is the derivative of sinx?
100
f'(c) = f(b) - f(a)/(b-a})
What is the Mean value theorem?
100
( f (x) ∙ g(x) ) ' = f ' (x) g(x) + f (x) g' (x)
What is the Derivative product rule?
100
The integral of [x/(x^4 + 1)] dx
What is u=x^2
100
Inventor of Calculus
Who is Sir Isaac Newton?
200
-sinx
What is the derivative of cosx?
200
Let f be continuous on a closed interval [a, b] and differentiable on the open interval (a, b). If f(a) = f(b), then there is at least one point c in (a, b) where f '(c) = 0.
What is Rolle's Theorem?
200
f ( g(x) ) ' = f ' ( g(x) ) ∙ g' (x)
What is the Derivative chain rule?
200
The integral of [(2x + 2)(e^(x^2 + 2x + 3)) dx]
What is u=x^2 + 2x + 3
200
Egyptian Moscow papyrus (c. 1820 BC)
What is The place that the first precursor of calculus was found?
300
(secx)(tanx)
What is the derivative of secx?
300
V=2π∫[radius] [shell height] dy from c to d
What is Shell method on the y axis?
300
( a f (x) + bg(x) ) ' = a f ' (x) + bg' (x)
What is Derivative sum rule?
300
The integral of [ x(2x+1)^(1/2) dx]
What is u=2x+1
300
General term used to refer to any body of mathematics
What is calculus before the invention of modern calculus?
400
sec^2(x)
What is the derivative of tanx?
400
= -1/(√(1−x^2)
What is The derivative of arc cos x?(Or arc -sin x)
400
d/(dx)[(f(x))/(g(x))]=(g(x)f^'(x)-f(x)g^'(x))/([g(x)]^2).
What is the Derivative quotient rule?
400
The integral of [x^3/((1+x^4)^(1/3))] dx
What is u=1+x^4
400
Methodus Fluxionum et Serierum Infinitarum
What is the first book Newton published about calculus?
500
-csc^2(x)
What is the derivative of cotx?
500
1/2(x + sin x cos x) + C
What is The integral of cos^2 x dx
500
Integration by parts formula
What is int(u*dv)=uv-int(v*du).
500
The integral of [(x^4 + 4x^2 + 5)(x^3 + 2x) dx]
What is u=x^4 + 4x^2 + 5
500
The other inventor of calculus
Who is Gottfried Leibniz?