Calc 2 formulas

memorize for calc 2

Find tangent line

1. derivative

2. find m by plugging x

3. y=mx+b -> plug, solve for b

4. rewrite y=mx+b

tangent line

A line that intersects a curve once and only once

secant line

the line through two points on a curve that approximates the slope of the curve between those points.

Derivative:

(Xⁿ)’

n(X^n-1)

Derivative:

(a^x)’

ln_a(a^x), a>0

Derivative:

(e^x)’

e^x

Derivative:

(log_aX)’

1/xln_a

Derivative:

f’(lnx)

1/x

Derivative:

f’(sinx)

cosx

Derivative:

f’(cosx)

-sinx

Derivative:

f’(tgx)

1/cos²x

Derivative:

f’(cotgx)

-1/sin²x

Derivative:

f’(arcsinx)

Derivative:

f’(arcosx)

Derivative:

f’(tanx)

Derivative:

f’(tanx)

Derivative:

f’(arccotx)

derivative of u:

(uⁿ)’

Integral of:

n cannot equal -1

Integral of:

Integral of:

Find integral of derivative

Find integral of derivative

Find integral of derivative

What is a derivative

Used to find the slope of a function at point. {an exact rate of change}

What is an integral (antiderivative)

The area under a curve of a graph that is integrated. Adds up tiny pieces to find a whole.

how are integrals and derivatives related

Are opposite operations that cancel each other out

f’(secx)

secxtanx

f’(cscx)

-cscxcotx

-cotx + C

secx + C

-cscx + C

derivative of:

sin^-1x

derivative of:

tan^-1x

sin^-1x + C

derivative of:

sec^-1x

tan^-1x + C

sec^-1x + C

Integration by parts

Integration by parts priority

sin²(x) + cos²(x)=

1

tan²(x) + 1=

sec²(x)

Integral

sin(x) + c

tan(x) + C

sec(x) + C

-cos(x) + C