Derivative Formulas AB Calc

ur cooked

Chain Rule: d/dx[f(g(x))]

F’[g(x)] * g’(x)

Constant Rule: d/dx[c]

0

Power Rule: d/dx[u^n]

n * u^n-1 * u’

Trig Rules: d/dx[sin(u)]

cos(u) * u’

Trig Rule: d/dx[cos(u)]

-sin(u) * u’

Trig Rule: d/dx[tan(u)]

sec²u * u’

Trig Rule: d/dx[cot(u)]

-csc²u * u’

Trig Rule: d/dx[sec(u)]

sec(u)tan(u) * u'

Trig Rule: d/dx[csc(u)]

-csc(u)cot(u) * u’

Exponent Rule with variable E: d/dx[e^u]

e^u * u’

Exponent Rule with Constant: d/dx[a^u]

a^u * u’ * ln(a)

Natural Log Rule: d/dx[ln(u)]

u’/u

Logarithmic Rule: d/dx[log_au]

u’/u * 1/ln(a)

Product Rule: d/dx[f(x)g(x)]

f(x) * g’(x) + g(x) * f’(x)

Quotient Rule: d/dx[f(x)/g(x)]

[g(x) * f’(x) - f(x) * g’(x)]/ [g(x)]²

Inverse Rule: d/dx[f^-1(x)]

1/f’(f⁻1(x))

Inverse Trig Rule: d/dx[sin^-1(u)]

u’/sqrt1-u²

Inverse Trig Rule: d/dx[cos^-1(u)]

-u’/sqrt1-u²

Inverse Trig Rule: d/dx[tan^-1(u)]

u’/1+u²

Inverse Trig Rule: d/dx[cot^-1(u)]

-u’/1+u²

Inverse Trig Rule: d/dx[sec^-1(u)]

u’/|u|sqrtu²-1

Inverse Trig Rule: d/dx[csc⁻1(u)]

-u’/|u|sqrtu²-1