One of the modern co-founders of the Calculus and the Laws of Motion
Who is Sir Issac Newton
200
$$x^{10}\cos{x}$$
What is $$10x^{9}\cos{x} - x^{10}\sin{x}$$
200
$$\sqrt[3]{x-5+15x^{4}}$$
What is $$\frac{1}{3}(x-5+15x^{4})^{-2/3}(1+60x^{3})$$
200
$$y=2e^{3x},\hbox{ at } x = 0$$
What is $$y = 6x+2$$
200
$$\cos{(y)} = \sin{(2x)}$$
What is $$y' = -\frac{2\cos{(2x)}}{\sin{y}}$$
200
The other modern cofounder; we're thankful for some of his notation.
Who is Gottfried Leibniz
300
$$\frac{2+x - 5x^3+x^4}{1-x^3}$$
What is $$\frac{(1 - 15x^2+4x^3)(1-x^3)-(2+x - 5x^3+x^4)(-3x^2)}{(1-x^3)^2}$$
300
$$e^{\tan{(x^{2}+4x -1)}}$$
What is $$(e^{\tan{(x^{2}+4x -1)}})(\sec^{2}{(x^{2}+4x -1)})(2x+4)$$
300
$$y = \cos{x}, \hbox{ at } x = \pi/6$$
What is $$y = -\frac{1}{2}(x -\pi/6) + \frac{\sqrt{3}}{2}$$
300
$$x^{3} - 5xy -y^{2} = 0$$
What is $$y' = \frac{3x^{2}-5y}{5x + 2y}$$
300
Now attributed with the invention of integration in classical Greece thanks to a prayerbook.
Who is Archimedes of Syracuse
400
$$5^{2-x}$$
What is $$(-\ln{5} 5^{2-x}$$
400
$$(x^{2} + \sqrt{x^{2}+1})^{17}$$
What is $$17(x^{2} + \sqrt{x^{2}+1})^{16}(2x + \frac{2x}{2\sqrt{x^{2}+1}})$$
400
$$y = \frac{1}{x^{2}}\hbox{ at } x = 3$$
What is $$ y = -\frac{2}{27}(x-3) + \frac{1}{9}$$
400
$$xe^{y} = \ln{(2 - 4x)}$$
What is $$y' = -\frac{e^{y}+\frac{4}{2-4x}}{x}$$
400
These ancient peoples used basic principles of the calculus to plot the movements of Jupiter.
Who were the Babylonians
500
$$(1-4x)^{3}(2x^{2}+2x)^{7}e^{5-x^{-1}}$$
What is $$-12(1-4x))^{2}(-4)(2x^{2}+2x)^{7}e^{5-x^{-1}}+ (1-4x))^{3}7(2x^{2}+2x)^{6}(4x+2)e^{5-x^{-1}}+ (1-4x))^{3}(2x^{2}+2x)^{7}\frac{1}{x^{2}}e^{5-x^{-1}}$$
500
$$\cos{(\sin{(x)}\cos{(x)})}$$
What is $$-\sin{(\sin{(x)}\cos{(x)})}(\cos^{2}{(x)}-\sin^{2}{(x)} )$$
500
$$y = 3\ln{(2x + 1)},\hbox{ at } x = 0$$
What is $$y = 6x$$
500
$$ y = x^{1-x}$$
What is $$y ' = (-\ln{x}+\frac{1-x}{x})x^{1-x}$$
500
We're thankful this mathematician simplified the notation used extensively in the Calculus