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Worksheet by Kuta Software LLC. Kuta Software - Infinite Calculus. Name___________________________________. Period____. Date________________. Logarithmic Differentiation. Use logarithmic differentiation to differentiate each function with respect to x. 1) y = 2x. 2x dy dx. = y(2ln x + 2). = 4x. 2x(ln x + 1). 2) y = 5x.
x. 3. f(t)=2t3 ? 4t2 + 3t ? 1. Also find f (t). Answer: f (t)=6t2 ? 8t + 3, f (t) = 12t ? 8. 4. y = v x ? (1. 2. )x. Answer: dy dx. = 1. 2. v x. + ln(2)(1. 2. )x. 5. f(z) = ln(3)z2 + ln(4)ez. Answer: f (z) = 2 ln(3)z + ln(4)ez. 6. y = x?2. + (?2)x. Answer: dy dx. = ?2x?2?1 + [ln(?2)](?2)x. 7. f(?)=4. v ?. Answer: f (?) = ln(4). 1. 2. v ?. 4. v ?. 1
that you undertake plenty of practice exercises so that they become second nature. After reading this text, and/or viewing the video tutorial on this topic, you should be able to: • differentiate ln x from first principles. • differentiate ex. Contents. 1. Introduction. 2. 2. Differentiation of a function f(x). 2. 3. Differentiation of f(x) = lnx.
ex ln a. Use chain rule and the formula for derivative of ex to obtain that y/ = ex ln a lna = ax lna. Thus the derivative of ax is ax lna. Derivative of the inverse function. . Practice Problems: 1. Find the derivatives of the following functions. In parts (g), (h) and (p) a and b are arbitrary constants. (a) y = (x2 + 1)e3x. (b) y = ex2+3x.
The rules of differentiation are straightforward, but knowing when to use them and in what order takes practice. Although the chain rule is no more com- plicated 5x7/2 -2x3/2 +4x-3/2 -8x-5/2. Hint. Answer. 15. ex lnx. Hint. Answer. 16. e2x + ln(x2 + 1). Hint. Answer. 17. sinet + coset. Hint. Answer. 18. ln(tanx + secx). Hint.
Differentiation by taking logarithms mc-TY-difftakelogs-2009-1. In this unit we look at how we can use logarithms to simplify certain functions before we differ- entiate them. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.
Page 1. AP Calculus AB - Worksheet 27. Derivatives of ln and e. Know the following theorems: 1. 2. Examples. 1. 2. 3. Find . 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. A line with slope m passes through the origin and is tangent to . What is the value of m? 18. Evaluate. Page 2. Answers.
Worksheet by Kuta Software LLC. Kuta Software - Infinite Calculus. Name___________________________________. Period____. Date________________. Differentiation - Natural Logs and Exponentials. Differentiate each function with respect to x. 1) y = ln x. 3. 2) y = e. 2x3. 3) y = ln ln 2x. 4. 4) y = ln ln 3x. 3. 5) y = cos
Math 1300. Derivative Practice for Final Exam. Name: Solutions. Some basic derivatives to know: • Power Functions: xn d dx. [ xn]. = nxn?1. • Exponential Functions and Logarithms: ex, ax, ln(x) d dx. [ ex]. = ex d dx. [ ax]. = (lna)ax d dx. [ ln(x). ] = 1 x. • Trigonometric Functions: sin(x), cos(x), tan(x) d dx. [ sin(x). ] = cos(x) d dx.
If you are not familiar with exponential and logarithmic functions you may wish to consult the booklet Exponents and Logarithms which is available from the Mathematics Learning. Centre. You may have seen that there are two notations popularly used for natural logarithms, loge and ln. These are just two different ways of
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