Just d/dx
Bound by the Chain Rule
The Theory of Us
Implicitly Difficult
Differentiation in Reverse
100
$$x^{\pi}\ln{(5-x)}$$
What is $$\pi x^{\pi -1}\ln{(5-x)} -\frac{x^{\pi}}{5-x}$$
100
$$e^{\left(\frac{2x+1}{x-1}\right)}$$
What is $$\frac{2(x-1)-(2x+1)}{(x-1)^{2}}e^{\left(\frac{2x+1}{x-1}\right)}$$
100
When $$\lim_{x \rightarrow a}f(x) = f(a)$$
What is f is continuous at a.
100
$$\frac{x^{2}}{12} + \frac{y^{2}}{8} = 1$$
What is $$y' = -\frac{2x}{3y}$$
100
$$4x^{3} - \frac{1}{x^{2}}$$
What is $$x^{4} + \frac{1}{x}$$
200
$$\frac{\tan{x}}{x^{2} + x -2}$$
What is $$\frac{(x^{2} + x -2)\sec^{2}{x} - (2x + 1)\tan{x}}{(x^{2}+x -2)^{2}}$$
200
$$\sqrt[5]{(6x -x^{3})^{4}}$$
What is $$\frac{4}{5}(6x -x^{3})^{(-1/5)}(6-3x^{2})$$
200
When $$\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}$$ exists.
What is f is differentiable at x.
200
$$\cos{(y)} = \sin{(2x)}$$
What is $$y' = -\frac{2\cos{(2x)}}{\sin{y}}$$
200
$$\sin{x}$$
What is $$-\cos{x}$$
300
$$\arctan{(x^{2})}$$
What is $$\frac{2x}{1 + x^{4}}$$
300
$$\arcsin{(\ln{(1-x^{2})})}$$
What is $$\frac{-2x}{(1-x^{2})\sqrt{1 - (\ln{(1-x^{2})^{2}}}}$$
300
The theorem that lets you conclude a continuous function has a root on any interval on which its value changes sign
What is the Intermediate Value Theorem
300
$$x^{4} - 12xy^{2} +y^{3} = 0$$
What is $$y' = \frac{4x^{3} - 12y^{2}}{24xy - 3y^{2}}$$
300
$$\frac{1}{2 \sqrt{2-x}}$$
What is $$-\sqrt{2-x}$$
400
$$10^{4x -5x^{2}}$$
What is $$\ln{10}(4-10x) 10^{4x -5x^{2}}$$
400
$$x + \sqrt{x+\sqrt{x}}$$
What is $$1+ \frac{(1+ \frac{1}{2\sqrt{x}})}{2\sqrt{x + \sqrt{x}}}$$
400
When $$f'(2) = 0,\hbox{ and } f''(2) = 6$$
What is f has a local minimum at 2
400
$$x\sin{y} = y\cos{x}$$
What is $$y' = -\frac{\sin{y} + y\sin{x}}{x\cos{y} - \cos{x}}$$
400
$$\frac{1}{x+3}$$
What is $$\ln|x+3|$$
500
$$x^{\sin{x}}$$
What is $$(\cos{x}\ln{x} + \frac{\sin{x}}{x})x^{\sin{x}}$$
500
$$\sin{x}\ e^{\cos{x}} + \cos{x}\ e^{-\sin{x}}$$
What is $$\cos{x}\ e^{\cos{x}}-\sin^{2}{x}\ e^{\cos{x}} -\sin{x}\ e^{-\sin{x}}-\cos^{2}{x}\ e^{-\sin{x}}$$
500
The theorem that helps us deduce what $$\lim_{h \rightarrow 0}\frac{\sin{h}}{h} = 1$$
What is the Squeeze (Sandwich) Theorem.
500
$$ y^{x}= x^{y}$$
What is $$y ' = \frac{\ln{y} -\frac{y}{x}}{\ln{x} - \frac{x}{y}}$$
500
$$5^{x+1}$$
What is $\frac{1}{\ln{5}}5^{x+1}$
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