Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx...

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Derivative Facts (1/23/12) d/dx (x r ) = (provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx (ln(x)) = d/dx (arcsin(x)) = d/dx (arctan(x)) =

description

Clicker Question 1 What is the derivative function of f (x ) = 5x sin(3x ) ? A. 5 cos(3x) B. 15 cos(3x) C. 15x cos(3x) + 5 sin(3x) D. 5x cos(3x) + 5 sin(3x) E. -5x cos(3x) + 5 sin(3x)

Transcript of Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx...

Page 1: Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx.

Derivative Facts (1/23/12) d/dx (x r ) = (provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx (ln(x)) = d/dx (arcsin(x)) = d/dx (arctan(x)) =

Page 2: Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx.

Derivative Rules Constant Multiplier Rule Sum and Difference Rule Product Rule Quotient Rule Chain Rule

Page 3: Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx.

Clicker Question 1 What is the derivative function of

f (x ) = 5x sin(3x ) ? A. 5 cos(3x) B. 15 cos(3x) C. 15x cos(3x) + 5 sin(3x) D. 5x cos(3x) + 5 sin(3x) E. -5x cos(3x) + 5 sin(3x)

Page 4: Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx.

Clicker Question 2 What is the exact instantaneous rate

of change of the function g (x ) = 2x

at the point x = 3? A. 8 ln(2) B. 6 ln(2) C. 8 D. 12 E. 12 ln(2)

Page 5: Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx.

Clicker Question 3 What is the slope of the tangent

line to the curve y = (x 2 + 3) when x = 2 ? A. 1 / (27) B. 47 C. 27 D. 2 /7 E. 1 / (47)

Page 6: Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx.

A Sample Pointing Our Direction This Semester

From your MA 108 final exam:

Find all the points in the domain of f (x) = x 4/4 + x 3 – 2x 2 + 7 at which the tangent line is horizontal.

These points are critical. We shall talk about why they are important this semester, along with various other ideas.

Page 7: Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx.

Assignment for Wednesday

Go over your MA 108 final exam and correct it.


wk3sn2fall2015 - Department of Mathematics - …swheeler/math 1431/Completed...xx x x dx dx dx ddd xx x x dx dx dx dd cx c x dx dx fg f g fg f g ff += + −= − = = d 8 dx = d x dx

wk3sn2fall2015 - Department of Mathematics - …swheeler/math 1431/Completed...xx x x dx dx dx ddd xx x x dx dx dx dd cx c x dx dx fg f g fg f g ff += + −= − = = d 8 dx = d x dx

Midterm Review. Calculus Derivative relationships d(sin x)/dx = cos x d(cos x)/dx = -sin x.

Midterm Review. Calculus Derivative relationships d(sin x)/dx = cos x d(cos x)/dx = -sin x.

Agfa-Gevaert · 2017. 1. 19. · solutions in 2011. Examples are the next generation CR 30-X, the automated DX-D 600 DR room, the mobile DX-D 100 DR system and the wireless DX-D 30

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x) · cot x = ¯csc 2 x d dx sec x = sec x tan x f(t) = 1 2 gt 2 + v 0 t + s0 v(t) = f'(t) a(t) = v'(t) = f"(t) d dx csc x = ¯csc x cot x d dx (f(x)⋅g(x))= f(x)g'(x)+ g(x)f'(x)

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1.- · 2021. 2. 24. · Bloque 4) 3 In x2 +1 + k dx Determina estas integrales de funciones racionales. dx dx=41n x —2 + k dx x dx In x dx = dx In x x + dx x x — arc tg x dx =

integration indefinite mix student version · 2018. 2. 5. · 2 2 1 cos tan dx ∫ x x 193. ∫ 3cos 33 x dx 194. ∫ 3sec 4 x dx 195. ∫ 2sin cos3x x dx 196. 2sin cos sin x dx ∫

integration indefinite mix student version · 2018. 2. 5. · 2 2 1 cos tan dx ∫ x x 193. ∫ 3cos 33 x dx 194. ∫ 3sec 4 x dx 195. ∫ 2sin cos3x x dx 196. 2sin cos sin x dx ∫

Integral ch 7 - ncert.nic.inncert.nic.in/textbook/pdf/lemh201.pdf · ∫f x dx() Integral of f with respect to x f(x) in ∫f x dx() Integrand x in ∫f x dx() Variable of integration

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FMSP FP3 Revision Day 1 - mrvahora · FMSP FP3 Revision Day 5 9. Derivatives of the inverse hyperbolic functions: d dx arsinh x 1 1 x2 d d x arcosh x 1 2 1 d dx artanh x 1 1 x2 10.

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xy y2 dx x

xy y2 dx x

Today: 6.2 Trig substitution · Today: 6.2 Trig substitution Warm up: 1.Calculate the following integrals. (a) Z cos2(x) dx (b) Z cos2(x)sin2(x) dx (c) Z cot2(x) dx (d) Z tan3(x)

Today: 6.2 Trig substitution · Today: 6.2 Trig substitution Warm up: 1.Calculate the following integrals. (a) Z cos2(x) dx (b) Z cos2(x)sin2(x) dx (c) Z cot2(x) dx (d) Z tan3(x)

4 !: :wu ü - GitHub Pages · « 4. 1 D = {(x ,y) | 1 ! x ! 2, 0 ! y ! 1} qb qz! ! D (x 2 + x y + y2)dx dy =! 2 1" ! 1 0 (x 2 + x y + y2)dy dx =! 2 1 (x 2 y + 1 2 x y2 + 1 3 y3) 1

4 !: :wu ü - GitHub Pages · « 4. 1 D = {(x ,y) | 1 ! x ! 2, 0 ! y ! 1} qb qz! ! D (x 2 + x y + y2)dx dy =! 2 1" ! 1 0 (x 2 + x y + y2)dy dx =! 2 1 (x 2 y + 1 2 x y2 + 1 3 y3) 1

SEM-2410/X/D/DX Wireless Ethernet Bridge

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 · Exercise 5.3 2x + 3y = sin x Differentiating both sides with respect to x, we get — sin x dx dx dx dy cosx — 2 dx 2x + = sin y dy dx cos x Question 2: 2x + = sin y Answer

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