Let f(x)=(x? + 1)^(2x – 1) is a polynomial function of fifth degree. Its second derivative...
ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A. dx 8 X xf (x) 7f(x) dy O B. dx 8 X dy xf(x) 7f(x) O C. dx 8 X 7f'(x) xf(x) dy O D. dx 8 X ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A....
dy For the following composite function, find an inner function u = g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dx y=tan (2x) Calculate the derivative of the following function. y = (5x - 19) dy Carry out the following steps for the given curve. dy a. Use implicit differentiation to find dx b. Find the slope of the curve at the given point. x +y = 337;( - 4,3) a. Use implicit differentiation to find b....
3. (a) Let f be an infinitely differentiable function on R and define х F(x) = e-y f(y) dy. Find and prove a formula for F(n), the nth derivative of F. (b) Show that if f is a polynomial then there exists a constant C such that F(n)(x) = Cem for sufficiently large n. Find the least n for which it is true.
Let D P3P3 be the function that sends a polynomial of degree 3 to its derivative (a) Find an eigenvector for D or explain why no eigenvector exists Write your solution here (b) Let B 1 x, x + x2, x2 + x3,x3}. B is a basis for P3. Find MDB-B Here, MD.- is the unique matrix such that MD-xs = [D(x)]s Write your solution here Recall that D: P is polynomial differentiation. 1x, x +x2, x2 +x3,x3} and C...
Find the second-order partial derivative. Find fxy when f(x,y) = 8x®y - 7y2 + 2x. O A. 24x? B. 48xy O C. - 14 OD. -28
3. (a) Let f be an infinitely differentiable function on R and define F(x) = [-vf(u) dy. Find and prove a formula for F(n), the nth derivative of F. (b) Show that if f is a polynomial then there exists a constant C such that F(n)(x) = Cea for sufficiently large n. Find the least n for which it is true.
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
ax az . Letſ be a differentiable function of one variable, and let w = f(p), where p = (x2 + y2 + 2)/2. Show that dw ay · Let z = f(x - y. y - x). Show that az/ax + az/ay=0. Let f be a differentiable function of three variables and sup- pose that w = Sex - y. y - 2.2 - x). Show that aw ду az Page 1 / 1 aw aw ax + +...
The directional derivative of the function f(x, y) = 2x In(y) in the direction v =< 0,1 > at the point (1,1) is equal to 2. Select one: O True False
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...