BC Calc Formula Test

d/dx [cu] =

cu'

d/dx [u+/-v] =

u' +/-v'

d/dx [uv] =

uv' + vu'

d/dx [u/v] =

(vu'-uv')/v²

d/dx [c] =

0

d/dx [u^n] =

nu^(n-1)(u’)

d/dx [x] =

1

d/dx [|u|]

(u/|u|) u'

d/dx [ln u] =

u'/u

d/dx [e^u] =

e^u u'

d/dx [log (base a) (u)] =

u'/u ln a

d/dx [a^u] =

ln(a) a^u u'

d/dx [sin u] =

cos(u) u'

d/dx [cos u] =

-sin(u) u'

d/dx [tan u] =

sec²(u) u'

d/dx [cot(u)] =

-csc²(u) u'

d/dx [sec(u)] =

sec(u)tan(u) u'

d/dx [csc u] =

-(csc(u)cot(u)) u'

d/dx [sin⁻¹(x)] =

u'/√(1 - u²)

d/dx [cos⁻¹(x)] =

-u'/√(1 - u²)

d/dx [tan⁻¹(u)] =

'u/(u²+1)

d/dx [cot⁻¹(u)] =

-u'/(u^2+1)

d/dx [sec⁻¹(u)] =

u'/|u|(√u^2-1)

d/dx [csc⁻¹(u)]

-u'/|u|(√u^2-1)

∫k f(u) du =

k ∫f(u) du

∫[f(u) ± g(u)]du =

∫f(u)du ± ∫g(u)du

∫ du =

u + C

∫uⁿ du =

uⁿ⁺¹/(n+1) + C, n ≠ −1

∫ du/u =

ln|u| + C

∫ eᵘ =

eᵘ + C

∫ aᵘ du=

(1/ln a)·aᵘ + C

∫ sin u du =

−cos u + C

∫ cos u du =

sin u + C

∫ tan u du =

-ln |cos u| + C

∫ cot u du =

ln |sin u| + C

∫ sec u du =

ln |sec u + tan u| + C

∫ csc u du =

-ln |csc u + cot u| + C

∫ sec² u du =

tan u + C

∫ csc² u du =

-cot u + C

∫ sec u tan u du =

sec u + C

∫ csc u cot u du =

-csc u + C

∫ du/√(a²-u²) =

arcsin(u/a) + C

∫ du/(a²+u²) =

1/a arctan(u/a) + C

∫ du/u√(u²-a²) =

1/a arcsec(|u|/a) + C

Taylor Series centered at x =c

(f^(n)(c))/n! (x-c)^n, f(c) + f'(c)(x-c) + f"(c)/2! (x-c)^2 +…

Derive a series for e^x

x^n/n!, 1 + x + x^2/2! …

Derive a series for cos x

x^2n * (-1)^n/2n!

Derive a series for sin x

x^2n+1 * (-1)^n/(2n+1)!