Limits & Differentiation Limits of Functions II Lowersixth Science Mathematics

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Limits & Differentiation Limits of Functions II Lowersixth Science Mathematics


Froggy Jumps Limits & Differentiation Limits of Functions II Lowersixth Science MathematicsOnline version Core differentiation topics practice. by YAKILI LMS 1 What is the quotient rule formula for d/dx of u/v? a (uv' - u'v)/v^2 b (u'v - uv')/v^2 c (u' + v')/v 2 If y = (2x+1)/(x-3), y' equals? a (2(x-3) - (2x+1))/ (x-3)^2 b (2x-1)/(x-3)^2 c ((2x+1)'(x-3) - (2x+1)(x-3)')/ (x-3)^2 3 Which rule uses f(g(x)) derivative? a Quotient rule b Chain rule c Product rule 4 If y = sin(3x), y' = ? a 3cos(3x) b cos(3x) c sin(3x) 5 d/dx tan x is a 1/cos^2 x b sec^2 x c cos x 6 Derivative of cos x is a sin x b -sin x c -cos x 7 Derivative of \|x\| at x>0 is a 1 b -1 c 0 8 Derivative of \|x\| at x<0 is a 1 b 0 c -1 9 Implicit differentiation allows: a Solve y explicitly first b Differentiate only x c Differentiate without solving for y 10 If y^2 = x, dy/dx = a 1/(2y) b 2y c y/2x 11 Derivative of e^kx is a e^{kx} b k e^{kx} c e^{kx}/k 12 Derivative of ln x is a x b 1/ln x c 1/x 13 Chain rule example: d/dx of sin(2x) is a 2cos(2x) b 2sin(2x) c cos(2x) 14 If y = (x^2+1)^3, dy/dx = a 6x(x^2+1)^2 b 3x^2(x^2+1) c 3(x^2+1)^2 * 2x 15 Derivative of ln(x^2+1) is a 2x/(x^2+1) b x/(x^2+1) c 2/(x^2+1) 16 Quotient rule applies when differentiating a u+v b v/u c u/v 17 Derivative of arcsin x is a √(1-x^2) b 1/√(1-x^2) c 1/(1-x^2) 18 Derivative of arccos x is a 1/√(1-x^2) b -√(1-x^2) c -1/√(1-x^2) 19 Derivative of arctan x is a 1/(1-x^2) b 1/(1+x^2) c 1/x^2 20 Derivative of sqrt(x) is a √x b 2√x c 1/(2√x) 21 Implicit differentiation helps when a function is a Always explicit b Not easily solved for y c Linear 22 Derivative of x^n is a x^{n+1} b n x^{n-1} c n x^n 23 Derivative of a constant is a 0 b -1 c 1 24 Differentiating a product uv gives a u'v + uv' b u'v - uv' c u v' 25 Derivative of log base a of x is a ln x / a b a/x c 1/(x ln a) 26 Chain rule in form f'(g(x))g'(x) applies to a Composite functions b Linear equations c Rational functions 27 Derivative of sec x is a sec x tan x b cos x c sec x cot x 28 Derivative of csc x is a -csc x cot x b -sec x tan x c csc x cot x 29 Derivative of cot x is a -sec^2 x b csc^2 x c -csc^2 x 30 For y = u/v, dy/dx = a (uv')/v^2 b (u'v - uv')/v^2 c (u'v + uv')/v^2 31 If y = (3x+2)/(x^2+1), y' involves a Quotient rule b Chain rule c Product rule 32 Derivative of ln\|x\| is a x b 1/\|x\| c 1/x 33 Derivative of e^{ax+b} is a e^{ax+b}/a b e^{a}x+b c a e^{ax+b} 34 Derivative of e^{sin x} by chain rule is a cos x · e^{sin x} b e^{cos x} c sin x · e^{sin x} 35 Derivative of f(g(x)) is a f(g'(x)) b f'(x)·g'(x) c f'(g(x))·g'(x) 36 If y = cos(2x), y' = a -2sin(2x) b 2sin(2x) c -2cos(2x) 37 Derivative of \|u\| with respect to x is a u/\|u\| · du/dx b \|du/dx\| c du/dx 38 Total derivative uses a Chain rule and implicit differentiation b Only product rule c Only quotient rule 39 Derivative of x^0 is a 0 b 1 c x 40 Derivative of a constant multiple: d/dx(c·f(x)) a f(x)/c b c·f'(x) c f'(x)/c 41 Quotient rule requires a Only u differentiable b Both u and v differentiable c Only v differentiable 42 Derivative of arcsin x at x=0 is a 0 b -1 c 1 43 Derivative of arctan x at x=0 is a 0 b 1 c -1 44 Derivative of ln(u) is a u'/u b u/u' c u/ln u 45 Derivative of a constant inside abs value affects a Always 1 b Always 0 c Depends on sign of inner function 46 Chain rule is essential for a Nested functions b Linear functions only c Constants only 47 Derivative of x\|x\| is a x/\|x\| b 0 c 2x for x>0, 0 at x=0, 2x for x<0 48 Derivative of tanh x is a sech^2 x b tanh x c sech x 49 Derivative of cot x is a -sec^2 x b csc^2 x c -csc^2 x 50 Derivative of sec x is a sec x cot x b sec x tan x c tan x

Limits & Differentiation Limits of Functions II Lowersixth Science Mathematics

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Limits & Differentiation Limits of Functions II Lowersixth Science MathematicsOnline version

by YAKILI LMS

What is the quotient rule formula for d/dx of u/v?

If y = (2x+1)/(x-3), y' equals?

Which rule uses f(g(x)) derivative?

If y = sin(3x), y' = ?

d/dx tan x is

Derivative of cos x is

Derivative of |x| at x>0 is

Derivative of |x| at x<0 is

Implicit differentiation allows:

If y^2 = x, dy/dx =

Derivative of e^kx is

Derivative of ln x is

Chain rule example: d/dx of sin(2x) is

If y = (x^2+1)^3, dy/dx =

Derivative of ln(x^2+1) is

Quotient rule applies when differentiating

Derivative of arcsin x is

Derivative of arccos x is

Derivative of arctan x is

Derivative of sqrt(x) is

Implicit differentiation helps when a function is

Derivative of x^n is

Derivative of a constant is

Differentiating a product uv gives

Derivative of log base a of x is

Chain rule in form f'(g(x))g'(x) applies to

Derivative of sec x is

Derivative of csc x is

Derivative of cot x is

For y = u/v, dy/dx =

If y = (3x+2)/(x^2+1), y' involves

Derivative of ln|x| is

Derivative of e^{ax+b} is

Derivative of e^{sin x} by chain rule is

Derivative of f(g(x)) is

If y = cos(2x), y' =

Derivative of |u| with respect to x is

Total derivative uses

Derivative of x^0 is

Derivative of a constant multiple: d/dx(c·f(x))

Quotient rule requires

Derivative of arcsin x at x=0 is

Derivative of arctan x at x=0 is

Derivative of ln(u) is

Derivative of a constant inside abs value affects

Chain rule is essential for

Derivative of x|x| is

Derivative of tanh x is

Derivative of cot x is

Derivative of sec x is