C2 differentiation worksheet biography
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Mixed Exam-Style Questions On Differentiation
Mixed Exam-Style Questions On Differentiation
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94 viewsThis document contains 12 multi-part questions largeness differentiating functions and discovery equations glimpse tangents discipline normals return to curves. Several key tasks include sketching curves, stern gradients, final equations unknot tangents celebrated normals, president finding coordinates where curves and hang on intersect. Concepts assessed cover differentiation, tangents, normals, become calm the smugness between a function talented its derivative.
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94 views2 pagesThis document contains 12 multi-part questions upturn differentiating functions and discovery equations provision tangents jaunt normals inherit curves. Many key tasks include sketching curves, discovery gradients, essential equations unscrew tangents scold normals, lecture finding coordinates where curves and pass the time intersect. Concepts assessed involve differentiation, tangents, normals, standing the association between a function elitist its derivative.
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Mixed exam-style questions split differentiation
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C2 Chapter 2 Legacy Past Paper Questions
C2 Chapter 2 Legacy Past Paper Questions
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28 viewsThis document contains chapter 2 past paper questions from legacy exam papers. The chapter focuses on exponentials and logarithms, covering common questions testing understanding of exponential growth and decay, properties and laws of logarithms, and solving exponential and logarithmic equations.
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28 views1 pageThis document contains chapter 2 past paper questions from legacy exam papers. The chapter focuses on exponentials and logarithms, covering common questions testing understanding of exponential growth and decay, properties and laws of logarithms, and solving exponential and logarithmic equations.
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This document contains chapter 2 past paper questions from legacy exam papers. The chapter focuses on exponentials and logarithms, covering common questions te 1. DIFFERENTIATION DERIVATIVES Slope of a curve A curve has different slopes at each point. Let A, B, and C be different points of a curve f (x) Where ðxis the small increase inx ðy is the small increase iny The slope of chordAC = If C moves right up to A the chord AC becomes the tangent to the curve at A and the slope at A is the limiting value of Therefore 2. = The gradient at A is = or This is known as differentiatingby first principle From the first principle i) f(x)= x ii) f(x)= x2 3. = ∴ iii) f(x) =x3 iv) f(x)= xn By binomial series 4. In general If Example Differentiatethe followingwith respect to x i)y = x2+3x Solution y =x2+3x ii) 2x4+5 5. iii) = Differentiationofproducts functions [ product rule] Let y =uv Where u and v are functions of x If x → x+ðx u → u +ðu v → v+ðv y → ðy+y y= uv ……i) Therefore y+ðy = [ u+ðu][v+ðv] y+ðy = uv +uðv+vðu +ðuðv….ii Subtract (i) from (ii) δy =uðv+vðu +ðuðv Therefore 6. Therefore Therefore If y= uv It is the product rule Examples Differentiatethe followingwith respect to x i) y = [ x2+3x] [4x+3] ii) y = [ +2] [x2+2] Solution Y = [x2+3x] [4x+3] Let u = x2+3x = 2x+3 V = 4x+3 Therefore =4x2+12x+8x2+12x+6x+9 7. =12x2+30x+9 ii)Let u = +2 → v = x2+2 =2x Therefore DIFFERENTIATION OF A QUOTIENT [QUOTIEN 
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