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Section 1

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Product Rule

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Calculus Math

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Date created

Mar 1, 2020

Cards (10)

Section 1

(10 cards)

Product Rule

Front

Let f,g be differentiable. Let F(x) = f(x)g(x). Then F'(x)=g'(x)f(x)+f'(x)g(x)

Back

Quotient Rule

Front

Let f,g be differentiable. Let F(x)=f(x)/g(x). Then F'(x)=(g(x)f'(x)-f(x)g'(x))/[g(x)]^2

Back

tangent line at x=a

Front

The tangent line of f(x) at x =a is a line passing through (a, f(a)) with slope f'(a).

Back

differentiable on (a,b)

Front

A function f(x) is differentiable on (a,b) if f'(c) exists for all c E (a,b).

Back

Implicit Differentiation

Front

The process of finding the derivative of an equation in two variables.

Back

second derivative

Front

The derivative of the first derivative is called the second derivative.

Back

height of a free falling object

Front

An object on Earth is released from a height hsub0 in ft with an initial velocity of vsub0 in ft/sec. Then the height of a free-falling object in ft after t seconds can be approximated by -16t^2+vsub0t+hsub0

Back

secant line

Front

for a function f(x), any line that passes through two points on the curve is a secant line

Back

derivative

Front

the derivative of f(x) with respect to x at x=a is given by f'(x)=lim as x approaches a of f(x)-f(a)/x-a provided the limit exists or in general the derivative of f(x) is given by f'(x)=lim as h approaches 0 of f(x+h)-f(x)/h provided the limit exists

Back

Chain Rule

Front

let h(x)=f of g= f(g(x) where f, g be differentiable with respect to x. Then h'(x)= f'(g(x))(g'(x))

Back