1) Your friend was asked to use the limit process to find the derivative of f(x)...
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) =...
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....
5. Use the limit definition to find the derivative of f(x) = V3x + 2. (6 points) 6. Find the derivatives of the following functions. Do not simplify after taking the derivative. 5 points each a. f(x) = (4x2 +1) c. h(x) = arcsin(3x2+ 2x-1) b. h(x) = 3sec(x2)
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y) = 2 - 2x + 5y - 3x?y at a point (3.4). a. Find f (3.4). b. Find f (3.4). f|(3.4)=0 (Simplify your answer.) 13(3.4)=0 (Simplify your answer.)
Differentiate. #’s 1,3, and 5 please 5.S LALT 1-16 Differentiate 2. f(x) = x cos x + 2 tanx 1. f(x) = x2 sin x 3. f(x)ecos x 2 sec x 4. y csC x 6. g(0)= e'(tan 0 e) 5. y = sec 0 tan 0 cot t 5.S LALT 1-16 Differentiate 2. f(x) = x cos x + 2 tanx 1. f(x) = x2 sin x 3. f(x)ecos x 2 sec x 4. y csC x 6. g(0)=...
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 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
Signature: 19.( 9 marks) Find the derivative of the following functions. 1. V = 1 " b. y = sinsx - Cos 3x c. y = (sec 5x + tan-'(1 - x)) 20. (6 marks) Find the derivative of the following functions. a) y = ln(1 - 3x) + 4* b) y = -2x + 3x +1
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
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...