Calc Flashcards

f(x) = √x

f’(x) = 1 / 2√x

f’(x) = 1 / 2sqrt(x)

f(x) = 3√x

f’(x) = 3 / 2√x

f’(x) = 3 / 2sqrt(x)

f(x) = x²

f’(x) = 2x

f(x) = 1/√x

f’(x) = -1 / 2√x³

f’(x) = -1 / 2sqrt(x³)

f(x) = 2/x

f’(x) = -2/x²

f(x) = sin(x)

f’(x) = cos(x)

f(x) = cos(x)

f’(x) = -sin(x)

f(x) = e^x

f’(x) = e^x

f(x) = ln(x)

f’(x) = 1 / x

Derivative Power Rule

d/dx[f(x)g(x)]

f’(x)g(x) + g’(x)f(x)

Derivative Quotient Rule

d/dx[f(x) / g(x)]

f’(x)g(x) - g’(x)f(x) / g(x)²

d/dx[tan(x)]

sec²(x)

d/dx[cot(x)]

-csc²(x)

d/dx[sec(x)]

d/dx[1/cos(x)]

tan(x) * sec(x)

d/dx[csc(x)]

d/dx[1/sin(x)]

-cot(x) * csc(x)

ln(1)

0

f(x) = 1/2x

f’(x) = -1/2x²

sin²+cos²

1

∫cos(x)dx

sin(x)

∫sin(x)dx

-cos(x)

∫x²dx

x³/3

Area between curves equation

A = ^b∫_a[g(x)-f(x)]dx

Volume of a solid equation

A = π ^b∫_a[g(x)-f(x)]dx