calculus-derivatives.tex

"\frac{d}{dx}x^n = n x^{n - 1}" true
"\frac{d}{dx}c = 0" true
"\frac{d}{dx}x = 1" true
"\frac{d}{dx}\frac{1}{x} = - \frac{1}{x^2}" true
"\frac{d}{dx}\frac{1}{x^2} = - \frac{2}{x^3}" true
"\frac{d}{dx}\sqrt{x} = \frac{1}{2 \sqrt{x}}" true
"\frac{d}{dx}\frac{1}{\sqrt{x}} = - \frac{1}{2 x \sqrt{x}}" true
"\frac{d}{dx}e^x = e^x" true
"\frac{d}{dx}b^x = b^x \ln(b)" true
"\frac{d}{dx}\ln(x) = \frac{1}{x}" true
"\frac{d}{dx}\log_b(x) = \frac{1}{x \ln(b)}" true
"\frac{d}{dx}\sinh(x) = \cosh(x)" true
"\frac{d}{dx}\cosh(x) = \sinh(x)" true
"\frac{d}{dx}\tanh(x) = \operatorname{sech}^2(x)" true
"\frac{d}{dx}\operatorname{arcsinh}(x) = \frac{1}{\sqrt{1 + x^2}}" true
"\frac{d}{dx}\operatorname{arctanh}(x) = \frac{1}{1 - x^2}" true
"\frac{d}{dx}\sin(x) = \cos(x)" true
"\frac{d}{dx}\cos(x) = -\sin(x)" true
"\frac{d}{dx}\tan(x) = \sec^2(x)" true
"\frac{d}{dx}\sec(x) = \tan(x) \sec(x)" true
"\frac{d}{dx}\arcsin(x) = \frac{1}{\sqrt{1 - x^2}}" true
"\frac{d}{dx}\arctan(x) = \frac{1}{1 + x^2}" true