Unit 2 - Differentiation Fundamentals

y’ of sin(x)

cos(x)

y’ of cos(x)

-sin(x)

y’ of tan(x)

sec²(x)

y’ of cot(x)

-csc²(x)

y’ of sec(x)

sec(x) · tan(x)

y’ of csc(x)

-csc(x) · cot(x)

product rule - f(x) * g(x)

f’(x) · g(x) + f(x) · g’(x)

quotient rule - f(x) / g(x)

g(x) · f’(x) - f(x) · g’(x) / _g²(x)

y’ of e^x

e^x

y’ of ln(x)

1 / _x

y’ of log_ax

1 / _{x · ln(a)}

y’ of a^x

a^x · ln(a)

y’ of constant

0

power rule - x^c

c · x^c-1

differentiable definition

1. Must be continuous

2. lim _(x^-) f’(x) = lim _(x⁺) f’(x)

equation of tangent line - f(x) at x = a

y - f(a) = f’(a) (x - a)