1) find the derivative of both sides of the function
2) put all terms with a y prime on the same side (y prime aka derivative of y)
3) factor out a y prime
4) solve for y prime

Back

What is the Chain Rule? When can it be used?

Front

deriv of [f(g(x))]= deriv of f of g(x)*deriv of g(x)
It can be used anytime

Back

What is the Alternate Difference Quotient Equation and what does it find?

Front

limit of (f(x)-f(c))/(x-c) as x-->c
It is finding the slope of the tangent line at a particular x-value

Back

what is the Difference Quotient Equation(a.k.a the limit definition of a derivative) and what does it find?

Front

f'(x) = limit of (f(x+changex)-f(x))/(changex) as the
changex-->0
It is finding the slope of the tangent line everywhere

Back

Deriv of f(x)=tanx is?

Front

sec^2x

Back

What is the quotient rule?

Front

h(x)=(f(x))/(g(x))
derivative of h(x)=[g(x)deriv of f(x)]-[f(x)deriv of g(x)]/(g(x))^2

Back

Deriv of f(x)=cotx is?

Front

-csc^2x

Back

Deriv of f(x)=sinx is?

Front

cosx

Back

Deriv of f(x)=cosx is?

Front

-sinx

Back

Deriv of f(x)=secx is?

Front

tanxsecx

Back

What is the product rule?

Front

h(x)=f(x)*g(x)
derivative of h(x)=[f(x)deriv of g(x)]+[g(x)deriv of f(x)]

Back

implicit differentiation

Front

not clear; when you can solve for y as a function of x
EX) y^3+y^2-5y-x^2=4

Back

derivative

Front

slope of the tangent line

Back

When do derivatives not exist?

Front

1)At a "spot" of discontinuity (pt.(hole), infinite(VA), jump)
2)At a cusp(sharp pt.)
3)At a vertical tangent line

Back

explicit differentiation

Front

very clear; the variable y is explicitly written as a function of x and it only works when you can solve for the function explicitly
EX) y=3x^2-5