# Shared Flashcard Set

## Details

Calculus Basic Differentiation Rules
Basic Differentiation/Integration Formal Rules with follow up example
41
Mathematics
07/06/2019

Term
 d/dx [|u|] = ?
Definition
 d/dx [|u|] = (u/|u|)(u'), u ≠ 0
Term
 d/dx [ln u] = ?
Definition
 d/dx [ln u] = u'/u
Term
 d/dx [ln(5x3)] = ?
Definition
 d/dx [ln(5x3)] = 15x2/5x3 = 3/x
Term
 d/dx [eu] = ?
Definition
 d/dx [eu] = (eu)u'
Term
 d/dx[e(5x^3)] = ?
Definition
 d/dx [e5x^3] = (e5x^3)(15x2)
Term
 d/dx[logau] = ?
Definition
 d/dx[logau] = u'/(ln a)u
Term
 d/dx[log520x3] =
Definition
 d/dx[log520x3] = 60x2/(ln 5)20x3 = 3/(x(ln 5))
Term
 d/dx [sec u] = ?
Definition
 d/dx [sec u] = (sec u tan u)u'
Term
 d/dx [sec 2x8] = ?
Definition
 d/dx [sec 2x8] = (sec 2x8 tan 2x8)16x7
Term
 d/dx[csc u] = ?
Definition
 d/dx[csc u] = -(csc u cot u)u'
Term
 d/dx[csc 3x2] = ?
Definition
 d/dx[csc 3x2] = -(csc 3x2 cot 3x2)6x
Term
 d/dx[au] = ?
Definition
 d/dx[au] = (ln a)au u'
Term
 d/dx[53x^3] = ?
Definition
 d/dx[53x^3] = (ln 5)(53x^3)9x2
Term
 ∫eudu = ?
Definition
 ∫eudu = eu+C
Term
 ∫2e2xdx = ?
Definition
 ∫2e2xdx = e2x + C
Term
 ∫audu = ?
Definition
 ∫audu = au(1/ln(a)) + C
Term
 ∫55xdx = ?
Definition
 ∫55xdx = (1/5) (55x) (1/ln(5)) + C
Term
 ∫tan(u)du = ?
Definition
 ∫tan(u)du = -ln|cos(u)|+C
Term
 ∫tan(5x)dx = ?
Definition
 ∫tan(5x)dx = -(1/5)ln|cos(5x)| + C
Term
 ∫cot(u)du = ?
Definition
 ∫cot(u)du = ln|sin(u)|+C
Term
 ∫cot(8x)dx = ?
Definition
 ∫cot(8x)dx = (1/8)ln|sin(8x)| + C
Term
 ∫sec(u)du = ?
Definition
 ∫sec(u)du = ln|sec(u) + tan(u)| + C
Term
 ∫sec(25x)dx = ?
Definition
 ∫sec(25x)dx = (1/25) ln|sec(25x) + tan(25x)| + C
Term
 ∫csc(u)du = ?
Definition
 ∫csc(u)du = -ln|csc(u) + cot(u)| + C
Term
 ∫csc(2x)dx = ?
Definition
 ∫csc(2x)dx = (1/2) -ln|csc(2x) + cot(2x)| + C
Term
 ∫sec(u) tan(u) du = ?
Definition
 ∫sec(u) tan(u) du = sec(u) + C
Term
 ∫sec(51x) tan(51x) dx = ?
Definition
 ∫sec(51x) tan(51x) = (1/51) sec(51x) + C
Term
 ∫csc(u) cot(u) du = ?
Definition
 ∫csc(u) cot(u) du = -csc(u) + C
Term
 ∫csc(16x) cot(16x) dx = ?
Definition
 ∫csc(16x) cot(16x) dx = (1/16) - csc(16x) + C
Term
 logaxy = ?
Definition
 logaxy = logax + logay
Term
 logax/y = ?
Definition
 logax/y = logax - logay
Term
 loga1/x = ?
Definition
 loga1/x = -logax
Term
 logaxy = ?
Definition
 logaxy = y logax
Term
 What is the disk method for volumes of revolution around the horizontal axis?
Definition
 V=π∫x2dy
Term
 Think about how to come up the area of a circle by cutting the circle into a pie shape and turning it into a rectangle
Definition
Term
 What is the shell method to finding the volume through integration around the vertical axis?
Definition
 V=2π∫xy dy.  The equation must be substituted into the x value so that everything can be integrated with respect to y.
Term
 ∫du/(a^2+u^2) = ?
Definition
 (1/a)arctan(u/a) + C
Term
 cos2A = ?
Definition
 cos2A = 1/2 + (cos(2A))/2
Term
 sin2A = ?
Definition
 sin2A = 1/2 - (cos(2A))/2
Term
 1+tan2x = ?
Definition
 1+tan2x = sec2x
Term
 1+cot2x = ?
Definition
 1+cot2x = csc2x
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