Calc 1 Derivatives

ArcSin(u)

u’/square root(1-u²)

ArcCosu

-u’/square root(1-u²)

ArcTanu

u’/1+u²

ArcCotu

-u’/u² +1

ArcSecu

u’/absolute value (u) X square root (u² -1)

ArdCscu

-u’/absolute value (u) X square root (u²-1)

Inverse Theorum

g’(x)=1/f’(g(x))

E^x

e^x

e^u

u’e^u

a^x

a^x X ln(a)

a^u

a^u X u’ X ln(a)

ln(x)

1/x

ln(u)

u’/u

log base (a) of x

1/x X ln(a)

log base (a) of u

u’/u X ln(a)

Powers of Trig functions (sin(7x))²

Differentiate the power, differentiate trig function, differentiate input of the trig.

Basic chain Rule

Differentiate outer(leave inner alone) then multiply by the derivative of the inner

tan(x)

sec²(x)

cot(x)

-csc²(x)

sec(x)

sec(x)tan(x)

csc(x)

-csc(x)cot(x)

Area of a Circle

(pi)r²

Circumference of a circle

2(pi)r

Area of a rectangle

Length X Width

Area of a triangle

(1/2) X base X height

Volume of rectangular solid

length X width X height

volume of sphere

(4/3) X (pi)r³