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AP Calculus: Derivatives

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Section 1

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Guidelines for implicit differentiation

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Calculus Math

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Mar 1, 2020

Cards (16)

Section 1

(16 cards)

Guidelines for implicit differentiation

Front

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

Back

Deriv of f(x)=csc is?

Front

-cscxcotx

Back