Cambridge Additional Mathematics

Introduction to differential calculus (Chapter 13) 341 EXERCISE 13C 1 Using the graph below, find: a f(2) b f^0 (2) 2 Using the ...

342 Introduction to differential calculus (Chapter 13) 5aObserve the function f(x)=ex using the CD software. b What is the gradi ...

Introduction to differential calculus (Chapter 13) 343 ALTERNATIVE NOTATION If we are given a function f(x) then f^0 (x) represe ...

344 Introduction to differential calculus (Chapter 13) EXERCISE 13D 1 Find, from first principles, the gradient function of: a f ...

Introduction to differential calculus (Chapter 13) 345 The rules you found in theDiscoveryare much more general than the cases y ...

346 Introduction to differential calculus (Chapter 13) Example 5 Self Tutor If y=3x^2 ¡ 4 x, find dy dx and interpret its meanin ...

Introduction to differential calculus (Chapter 13) 347 Example 8 Self Tutor Find the gradient function for each of the following ...

348 Introduction to differential calculus (Chapter 13) 6 Find the gradient function of: a f(x)=4 p x+x b f(x)=^3 p x c f(x)=¡ 2 ...

Introduction to differential calculus (Chapter 13) 349 DERIVATIVES OF COMPOSITE FUNCTIONS The reason we are interested in writin ...

350 Introduction to differential calculus (Chapter 13) THE CHAIN RULE If y=g(u) where u=f(x) then dy dx = dy du du dx . This rul ...

Introduction to differential calculus (Chapter 13) 351 3 Find the gradient of the tangent to: a y= p 1 ¡x^2 at x=^12 b y=(3x+2)^ ...

352 Introduction to differential calculus (Chapter 13) 3 Copy and complete the following table, finding f^0 (x) by direct differ ...

Introduction to differential calculus (Chapter 13) 353 2 Find dy dx using the product rule: a y=x^2 (2x¡1) b y=4x(2x+1)^3 c y=x^ ...

354 Introduction to differential calculus (Chapter 13) Example 12 Self Tutor Use the quotient rule to find dy dx if: a y= 1+3x x ...

Introduction to differential calculus (Chapter 13) 355 EXERCISE 13H 1 Use the quotient rule to find dy dx if: a y= 1+3x 2 ¡x b y ...

356 Introduction to differential calculus (Chapter 13) Discovery 7 The derivative of y=bx The purpose of this Discovery is to ob ...

Introduction to differential calculus (Chapter 13) 357 We have already shown that if f(x)=bx then f^0 (x)=bx μ lim h! 0 bh¡ 1 h ...

358 Introduction to differential calculus (Chapter 13) c If y= e^2 x x then dy dx = e^2 x(2)x¡e^2 x(1) x^2 = e^2 x(2x¡1) x^2 fqu ...

Introduction to differential calculus (Chapter 13) 359 Discovery 8 The derivative of lnx If y=lnx, what is the gradient function ...

360 Introduction to differential calculus (Chapter 13) The laws of logarithms can help us to differentiate some logarithmic func ...