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Signature: 19.( 9 marks) Find the derivative of the following functions. 1. V = 1 "...
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y...
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y = 92 - 1 (b)r = (02 9016 /09 - 9 ( 9 ) (c) y=rºcot x + 9x2 cos x – 14x sin x 9t sint (d) s = cost + +9 (e) h(x) = cº sin (vą) + 240 sec (1) ) 10 (f) f(0) = (_sin 98 (1+cos 90 ) (g) g(x) = (1 + csc(+10) + In (922 – 8)...
10. Use the limit definition of the derivative to calculate the derivatives of the following functions....
10. Use the limit definition of the derivative to calculate the derivatives of the following functions. a. f(x) = 2x2 – 3x + 4 b. g(x) = = x2 +1 1 x2 +1 c. h(x) = 3x - 2 a. 11. Find the derivative with respect to x. x² - 4x f(x)= b. y = sec v c. 5x2 – 2xy + 7y2 = 0 1+cos x 1-cosx cos(Inu) e. S(x) = du 1+1 + + f. y =sin(x+y) g....
1. Find and simplify the derivative of each of the following functions: In(2 1) 2x 1)...
1. Find and simplify the derivative of each of the following functions: In(2 1) 2x 1) tan 1In(tan) (a) (x)In (b) f(x) = (412-1)3 In(4z?-1) (g) f(r)-n (n) f(x) = ln(sec 3r-tan 3r) 1 +x ln a
21. Find the derivative of each of the following functions by applying the product rule a....
21. Find the derivative of each of the following functions by applying the product rule a. f(x) = (x2 + 1][2x2 + 3x + 4) b. f(x) = x2 cos x c. f(x) = e* sin x 22. Find Find the derivative of each of the following functions by applying the quotient rule a. f(x) = 22+1 f(x) = (2x + 1] / [x - 3] b. f(x) = x+2x+1 3x + 1 c. f(x) = sing 23. Find the...
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 +...
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.
Question 4 [15 Marks) a. The voltage, v(t), across a capacitor varies with time, t, according...
Question 4 [15 Marks) a. The voltage, v(t), across a capacitor varies with time, t, according to v(t) = 2e-2t + 6 Calculate the average rate of change of the voltage from t = 1 to t = 2 b. Calculate the rate of change of y(x) = x2 + 2x when x = -5, without using the table of derivatives. C. Evaluate the following derivatives with the help of the table i. y = 2 tan+ y = 3x...
-/1 POINTS SCALC8 2.5.045. Find the derivative of the function. y = cos( V sin(tan(5x)))
-/1 POINTS SCALC8 2.5.045. Find the derivative of the function. y = cos( V sin(tan(5x)))
Show your work and CIRCLE or BOX your final answer. No credit if work is not...
Show your work and CIRCLE or BOX your final answer. No credit if work is not shown. Differentiate. 1) f(x) - 3x2 - 5x + 7 Basic Derivative Rules 1. (c)' = 0 2. Fix) + (x)] = f'(x) g'(x) 3. ) - 9(x)]* = f'() - g'(x) 4. Icf(x)]* = f'(x) 5. txx)-f(xlg'(x) + g(xY'x) f'(x)-f(x)g'(x) [g(x)] Derivatives of Trigonometric Functions sin(x) = cos(x) csc(x)=-csc(x)cot(x) * cos(x) = -sin(x) “sec(x) = sec(x) tan(x) tan(x) = sec (x) cot(x) =...
Q2) Find the derivative of each function a) f(1) = b) f(x) sin 1COSI 1+008 d)...
Q2) Find the derivative of each function a) f(1) = b) f(x) sin 1COSI 1+008 d) f(x) = (1 + x)'(1 - x)2 1 e) f(1) = 2009 1672 f). f() = ln(sec 0 + tan ) B): S(21) = 1n () h) y = (In(ax)? g(x) = ln(2.3 - 3x + 2) i) c) f(x) = sina
Use logarithmic differentiation to find the derivative of the function. y = (tan(x))2/ 4 cos ec(2x)...
Use logarithmic differentiation to find the derivative of the function. y = (tan(x))2/ 4 cos ec(2x) y' = 2 ln(tan(x)) 2 Need Help? Read It Watch It Talk to a Tutor Submit Answer 13. [1/1 Pointsi TOT
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y = 92 - 1 (b)r = (02 9016 /09 - 9 ( 9 ) (c) y=rºcot x + 9x2 cos x – 14x sin x 9t sint (d) s = cost + +9 (e) h(x) = cº sin (vą) + 240 sec (1) ) 10 (f) f(0) = (_sin 98 (1+cos 90 ) (g) g(x) = (1 + csc(+10) + In (922 – 8)...
10. Use the limit definition of the derivative to calculate the derivatives of the following functions. a. f(x) = 2x2 – 3x + 4 b. g(x) = = x2 +1 1 x2 +1 c. h(x) = 3x - 2 a. 11. Find the derivative with respect to x. x² - 4x f(x)= b. y = sec v c. 5x2 – 2xy + 7y2 = 0 1+cos x 1-cosx cos(Inu) e. S(x) = du 1+1 + + f. y =sin(x+y) g....
1. Find and simplify the derivative of each of the following functions: In(2 1) 2x 1) tan 1In(tan) (a) (x)In (b) f(x) = (412-1)3 In(4z?-1) (g) f(r)-n (n) f(x) = ln(sec 3r-tan 3r) 1 +x ln a
21. Find the derivative of each of the following functions by applying the product rule a. f(x) = (x2 + 1][2x2 + 3x + 4) b. f(x) = x2 cos x c. f(x) = e* sin x 22. Find Find the derivative of each of the following functions by applying the quotient rule a. f(x) = 22+1 f(x) = (2x + 1] / [x - 3] b. f(x) = x+2x+1 3x + 1 c. f(x) = sing 23. Find the...
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.
Question 4 [15 Marks) a. The voltage, v(t), across a capacitor varies with time, t, according to v(t) = 2e-2t + 6 Calculate the average rate of change of the voltage from t = 1 to t = 2 b. Calculate the rate of change of y(x) = x2 + 2x when x = -5, without using the table of derivatives. C. Evaluate the following derivatives with the help of the table i. y = 2 tan+ y = 3x...
-/1 POINTS SCALC8 2.5.045. Find the derivative of the function. y = cos( V sin(tan(5x)))
Show your work and CIRCLE or BOX your final answer. No credit if work is not shown. Differentiate. 1) f(x) - 3x2 - 5x + 7 Basic Derivative Rules 1. (c)' = 0 2. Fix) + (x)] = f'(x) g'(x) 3. ) - 9(x)]* = f'() - g'(x) 4. Icf(x)]* = f'(x) 5. txx)-f(xlg'(x) + g(xY'x) f'(x)-f(x)g'(x) [g(x)] Derivatives of Trigonometric Functions sin(x) = cos(x) csc(x)=-csc(x)cot(x) * cos(x) = -sin(x) “sec(x) = sec(x) tan(x) tan(x) = sec (x) cot(x) =...
Q2) Find the derivative of each function a) f(1) = b) f(x) sin 1COSI 1+008 d) f(x) = (1 + x)'(1 - x)2 1 e) f(1) = 2009 1672 f). f() = ln(sec 0 + tan ) B): S(21) = 1n () h) y = (In(ax)? g(x) = ln(2.3 - 3x + 2) i) c) f(x) = sina
Use logarithmic differentiation to find the derivative of the function. y = (tan(x))2/ 4 cos ec(2x) y' = 2 ln(tan(x)) 2 Need Help? Read It Watch It Talk to a Tutor Submit Answer 13. [1/1 Pointsi TOT
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