Questions on Differentiation (With Answers) · 1. Differentiate x5 with respect to x. Solution: Given, y = x · 2. Differentiate 10x2 with respect to x. Solution: ...
Justify your answer and state your conclusion. (b) Using the definition of the derivative, determine f (1). 5. Give one example of a function f(x) that is ...
Ch 5 Differentiation Multiple Choice Questions (With Answers) - Free download as PDF File (.pdf), Text File (.txt) or read online for free. XII CLASS CBSE MATHEMATICS Ch 5 Differentiation Multiple Choice Questions (With Answers)
DIFFERENTIAL EQUATIONS PRACTICE PROBLEMS: ANSWERS 1. Find the solution of y0 +2xy= x,withy(0) = −2. This is a linear equation. The integrating factor is e R 2xdx= ex2. Multiplying through by this, we get y0ex2 +2xex2y = xex2 (ex2y)0 = xex2 ex2y = R xex2dx= 1 2 ex2 +C y = 1 2 +Ce−x2. Putting in the initial condition gives C= −5/2,soy= 1 2 ...
Learning is a process, and getting answers to questions that you haven't considered on your ... 2.4 Arithmetic of derivatives - a differentiation toolbox .
Question 10 (****) Differentiate each the following expressions with respect to x, simplifying the final answers as far as possible. (Fractional answers must not involve double fractions) a) y x= sin 23. b) y x x= tan4 . c) 1 ln x y x + = . dy 6sin 2 cos22 x x dx = , tan4 4 sec 42 dy x x x dx = + , 2 dy 1 dx x x = − +
Drill problems on derivatives and antiderivatives 1 Derivatives Find the derivative of each of the following functions (wherever it is de ned): 1. f(t) = t2 + t3 1 t4 Answer: f0(t) = 2 t3 1 t2 + 4 t5 2. y= 1 3 p x + 1 4 ... Answer: f0(w) = 10wew2 + (5w2 + 3)2wew2 = (5w2 + 8)2wew2 11. f(y) = eey 2 Answer: f0(y) = 2yey2eey 2 12. f(z) = p z (ez+ 1 ...
DIFFERENTIATION PRACTICE QUESTIONS WITH ANSWERS. Find the derivatives of the following functions with respect to corresponding independent variables : Question 1 : Differentiate f(x) = x - 3 sinx. Solution : f(x) = x - 3 sinx. f'(x) = 1 - 3 cos x. Question 2 : …
1. Differentiation E. Solutions to 18.01 Exercises 7a 7b-3 -4 3 4 p 2p p 2p 1A-8 f(x) odd =⇒ f(0) = −f(0) =⇒ f(0) = 0. So f(c) = f(2c) = ··· = 0, also (by periodicity, where c is the period).
To build speed, try calculating the derivatives on the first sheet mentally … and have a friend or parent check your answers. If you are a teacher, please note that the sheets have been designed so that they may be laminated back-to-back (questions on one side and answers on the other) and used in a classroom setting.
l. Give your answer in the form 151 A is the point (2, 1) on the curve y — B is the point on the same curve with x-coordinate 2.1. (i) Calculate the gradient of the chord AB of the curve. Give your answer correct to 2 decimal places. [21 (ii) Give the x-coordinate of a point C on the curve for which the gradient of chord AC is a better
derivative of p 4x2 + 9. Answer. 13. Hint. 4x2 9 x2 16. Apply the quotient rule. An-swer. 14. Hint. 5x7=2 52x3=2 + 4x 3=2 8x =2. The power rule (x n)0= nx 1 works for fractional powers n. Just remember that nhas to be a constant, as it is here in each of …
Answer: (E) The limit of any constant function at any point, say f(x) = C, where C is an arbitrary constant, is simply C. Thus the correct answer is limx→2f(x) ...
Differentiation questions and answer - Free download as Word Doc (.doc / .docx), PDF File (.pdf), Text File (.txt) or read online for free. Thomas textbook.
1. Differentiate from first principles y = x2 − 4x. Answer. We have y + δy = (x + δx)2 − 4(x ... Applying the chain rule gives the derivative in question:.
17 Example: Find the gradient of the tangent to the curve y 2x3 3x2 7x 5 at the point (-2,5) Solution: y 2x3 3x2 7x 5 6x2 6x 7 dx dy At point (-2,5), x=-2 ...
Question 9 a) If A x x= −π 2 20 , find the rate of change of A with respect to x. b) If V x x= − 2π 3, find the rate of change of V with respect to x. c) If P at bt= −2, find the rate of change of P with respect to t. d) If 1 W kh h= −6 2 , find the rate of change of W with respect to h.
Question 9 (***+) The variables x and y satisfy the following coupled first order differential equations. 2 dx x y dt = − and 5 dy x y dt = − . Given further that x = − 1, y = 2 at t = 0, solve the differential equations to obtain simplified expressions for x and y. FP2-W , cos3 sin3 , 2cos3 sin35 7 3 3 x t t y t t= − − = −
11. Hint. p 1 x2.Another composition where the outer function is p and the inner function is 1 2x. Answer. 12. Hint. (4x2 9) p 4x2 + 9. You’ll need both the product rule and the chain rule for this.
Question 10 (****) Differentiate each the following expressions with respect to x, simplifying the final answers as far as possible. (Fractional answers must not involve double fractions) a) y x= sin 23. b) y x x= tan4 . c) 1 ln x y x + = . dy 6sin 2 cos22 x x dx = …
answers with those at the back of the booklet. The more questions that you attempt, the more familiar you will become with these vital topics. We have left sufficient space in the booklet so that you can do any necessary working within it. So, treat this as a work-book. If you get questions wrong you should revise the material and try again until