## FANDOM

150 Pages

For any constant a:

$a'=0$

For any real number r:

$(x^r)'=rx^{r-1}$ (Power rule)

For any real-valued differentiable functions $f(x)$ and $g(x)$:

• $a\,f'(x)=a\,f'(x)$
• $(f(x)+g(x))'=f'(x)+g'(x)$
• $\left(cf\right)' = c\left(f'\right)$ (Constant rule)
• $\left(-f\right)' = -\left(f'\right)$
• $\left(fg\right)' = f'g+fg'$ (Product rule)
• $\left( \frac 1 g \right)' = -\frac {g'} {g^2}$
• $\left( \frac f g \right)' = \frac {f'g-fg'}{g^2}$ (Quotient rule)
• $\left(f\circ g\right)' = \left(f'\circ g\right)g'$ (Chain rule)

Trigonometric functions:

• $(\sin(x))' = \cos(x)$
• $(\cos(x))' = -\sin(x)$
• $(\tan(x))' = \sec^2(x)$
• $(\csc(x))' = -\csc(x) \cot(x)$
• $(\sec(x))' = \sec(x) \tan(x)$
• $(\cot(x))' = -\csc^2(x)$
• $(\arcsin(x))' = \frac{1}{\sqrt{1-x^2}}$
• $(\arccos(x))' = -\frac{1}{\sqrt{1-x^2}}$
• $(\arctan(x))' = \frac{1}{1+x^2}$
• $(\arcsec(x))' = \frac{1}{|x|\sqrt{x^2-1}}$
• $(\arccsc(x))' = -\frac{1}{|x|\sqrt{x^2-1}}$
• $(\arccot(x))' = -\frac{1}{x^2+1}$

Logarithmic and exponential functions:

• $(e^x)'=e^x$
• $(a^x)'=a^x \ln(a)$
• $(\ln x)'=\frac{1}{x}$
• $(\log_{a}x)'=\frac{1}{x \ln(a)}$