CALCULUS: Graphical,Numerical,Algebraic b Finne,Demana,Watts and Kenned Chapter : Derivatives.: Derivative of a function pg. 116-16 What ou'll Learn About How to find the derivative of: Functions with positive and negative integer powers Functions with products and quotients A Using a definition of the derivative find the derivative of = at = a B Using a definition of the derivative find the derivative of = at = a C Using a definition of the derivative find the derivative of = + at = a 1 P a g e
Find the derivative using the power rule D f( = + - + 5 E 5 7 F G 5 1 H 1 f ( Find the Horizontal Tangents of each curve I + = 0 J 5 0 P a g e
Using Algebra and the Product Rule to take a derivative J = ( + ( - J = ( + ( - Using Algebra and the Quotient Rule to take a derivative K f ( 9 K f ( 9 Take the Derivative of the function L = ( + + ( 5 + + 5 P a g e
P a g e Take the Derivative of the function M ( f N 1 5 ( f O 1 ( f P 1 1 ( f
Find the equation for the tangent line at the given point 5 Q at = 1 R 5 at = S Find an equation of the line perpendicular to the tangent to the curve = - 6 + at the point (,. T Find the points on the curve = - - 9 where the tangent is parallel to the -ais 5 P a g e
U Suppose u and v are differentiable functions at = and u( =, u(, v(=1, v ( d d i Find uv ii Find d d u v d d iii Find u v uv V Find the derivative of = with respect to W Find the derivative of = with respect to t X Find the derivative of = with respect to P 6 P a g e
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CALCULUS: Graphical,Numerical,Algebraic b Finne,Demana,Watts and Kenned Chapter : Derivatives.5: Derivatives of Trig Functions pg. 11-17 What ou'll Learn About How to find the derivative of a trig function A = 5 + - tan B = sin C cot C cot D sin cos sec csc 9 P a g e
Find equations for the lines that are tangent and normal to the graph of = cos at Find the points on the curve = cot, 0, where the tangent line is parallel to the line = -. 10 P a g e
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CALCULUS: Graphical,Numerical,Algebraic b Finne,Demana,Watts and Kenned Chapter : Derivatives.6: Chain Rule pg.18-156 What ou'll Learn About How to find the derivative of a composite function A sin B sin C cos D csc cot 1 P a g e
1 P a g e cos sin 1 cos sin cos( sin( 5 F E E
G 1 G 1 H 5-15 P a g e
I - 6 5 J 1 1 16 P a g e
L csc M csc N Find if 9cot 17 P a g e
Suppose that functions f and g and their derivatives have the following values at = and =. Evaluate the derivatives with respect to A f( at B f( g( at C f(g( at D f( g( at 18 P a g e
E f g( at F f( at G 1 g at F f ( g ( at 19 P a g e
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CALCULUS: Graphical,Numerical,Algebraic b Finne,Demana,Watts and Kenned Chapter : Derivatives.8: Derivatives of Inverse Trig Functions pg.165-171 What ou'll Learn About How to find the derivative of inverse functions Find the derivative of the inverse sine function using implicit differentiation 1 P a g e
A arcsin B 1 arccos C arccos sin D 1- arctan E f( arccsc 5 sin Find the equation of the tangent line -1 F csc at P a g e
G Find the derivative of f( = sin at 6 H Find the derivative of f( = arcsin at 1 P a g e
-1. If f ( -, f (, and g( f (, what is the equation of the tangent line to g( at -? - - A - B C - D E - P a g e
- -1 5. If f ( -, f (, and g( f (, what is the equation of the tangent line to g( at -? - - A - B C - D E - - -1 6. If f ( -, f (, and g( f (, what is the equation of the tangent line to g( at -? - - A - B C - D - E - 5 P a g e
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7 P a g e CALCULUS: Graphical,Numerical,Algebraic b Finne,Demana,Watts and Kenned Chapter : Derivatives.9: Derivatives of Eponential and Logarithmic Functions 7 e - 5 5 6 5 7 5 5 5 arctan sin B e I e H e G e F e E D C B A What ou'll Learn About How to take the derivative of eponential and logarithmic functions
8 P a g e arcsin ln - ln n 5 ln ln ln ln log 5 log log log 7 5 6 5 l I H G F E D C B A
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CALCULUS: Graphical,Numerical,Algebraic b Finne,Demana,Watts and Kenned Chapter : Derivatives.6/10.1: Derivatives of Parametric Equations What ou'll Learn About How to take the derivative of functions in Parametric Form Graph the parametric function given A t - t t 0 B Find the derivative of the function at t=5 C Find the equation of the tangent line at t=1 t 9t D Find the equation of the tangent line at cos sin E Find the equation of the tangent line at t sec t -1 tan t 0 P a g e
A curve C is defined b the parametric equations = t t +1 and = t. Determine the equation of the line tangent to the graph of C at the point (1, 6? Determine the horizontal and vertical tangents for the parametric curve A 1- t t - t B cos sin 1 P a g e
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The derivative of e is: (Itself(Derivative of the power The derivative of a is: (Itself(ln of the base(derivative of the power The derivative of a is: (Itself(ln of the base(derivative of the power The derivative of ln u is: (one over what ou are taking the ln of times now ou should be in the numerator (Derivative of what ou are taking the ln of P a g e
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When ou do the power rule the base does not change onl the power - Once ou have done the power rule, ou are done with the powers When ou do the derivative of a trig function the angle does not change 5 P a g e
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