Question 17 Find the derivative of the function f(x) = 4e*cosx . Simplify your answer. 0...
Question 12 Find the derivative of the function f(x)= (in(cox) + sinº(x))2. • f'(x) = 12(In(cox) + sin?(x)) (3sin?x cosx – tanx) • f'(x) = 12(In(cox) + sin?(x))+(3sinx cos?x - tanx) o f'(x) = 12(In(cox) + sin(x))(3sinx cosx + tanx) o f'(x) = 12(In(cox) + sin}(x))^2(3sin?x cosx + tanx) A Moving to another question will save this response.
5. Jula found the derivative of some function and obtained the following: sinx f'(x) = 1+ cosx + 1+ cosx sinx Prove that the above derivative is the same as f'(x) = 2 csc(x)
Find the derivative of the function. F(x) = x – 5x V x √x (a) Simplify the function to the point where you will not need the Product or Quotient Rule (b) Use the part a), find the derivative of the function. F'(x) =
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
Consider the function f(x)-5x -x-3 and complete parts (a) through (d) (a) Find fix + h) (b) Find fkth) fs) (c) Use the above answer and the limit definition of the derivative to find the derivative of the function f (d) Find the value of the derivative of f when x-1 (a) fx+h)- Simplify your answer. Do not factor) fx+ h) fx) Simplify your answer Do not factor.) c) f(x) E (d) The derviative f(1) elfo Simplify your answer)
Consider the function f(x)-e a. Differentiate the Taylor series about 0 of f(x). b. Identify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. a. Choose the correct answer belovw 213 Ос. D. 2 41 61 b. The function represented by the differentiated series is Iill c. The interval of convergence of the power series for the derivative is Simplify your answer. Type an inequality or a compound inequality...
Find the derivative of the function. f(x) = (ln(x + 5)) f'(c) = Preview Find the derivative of the function. f(t) = ť(In(t))? f'(t) = Preview If f(a) = 8 ln(4x), find a. f b. Rounded to the nearest whole number: f(e) c. Rounded to the nearest whole number: f'(e) = d. sing your results for f(e) and f'(e), find the equation fo the line tangent to the curve f(x) at the point (e, f(e)). Round decimals to the nearest...
11. (5 points each) Find the derivative of each function. DO NOT simplify your answers. cos(x) a) f(x) = 1-tan(x) b) f(x) – tan-" (4x²) dy 12. Consider the equation x² + xy + y² = 1. Find an expression for by implicit differentiation. dx
Is x = 0 a relative extrema for function f : R → R that is given by f(x) = sinx − cosx − 1/2(1 + x)^2 Question 3. Is x = 0 a relative extrema for function f:R + R that is given by 1 COS X f(x) = sin x (1 + x)? 2 Prove your claim. State any theorem that is applied in your proof.
determine the slope of the tangent at x=0 for the function f(x)= cosx over 1-x (cosx ---------- 1-x)