Taking the derivative of x tan x and using the fact that tan x = (ln sec x) 0 allows us to anti-differentiate a certain function. What function is it?
Taking the derivative of x tan x and using the fact that tan x = (ln...
3.(30 pts.). Taking the derivative of atanz and using the fact that tan r = (In sec x)' allows us to anti-differentiate a certain function. What function is it? 4.(30 pts.) Let f(x) = (r? - 1)Find all solutions y of 1 = f(y) and state the domains and ranges of the resulting functions y = 9() which, by definition, satisfy f(g(2)) = 1
5. Find the derivative of f(x) = ln (sec(x) + tan *' (x)). 6. Find an equation of the tangent line to the curve y = x’ In(x) when x = e?
Q2 a) Find the second derivative of the following function y = tan x + sin-1x b) Using chain rule find any as function of y for the following function y = Vē – 1, x = t2 In x c) Using L'Hopital's rule find the limits as x approach 1 of the function d) find for the function y = ln xy + log10 (x + 3) + 2*+sinh-1x dx
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
Solve by using Cramer’s Rule 4 e x – 6 tan( y ) + 2 ln(z) = 1 3 e x + 5 tan( y ) – 3 ln(z) = 2 e x + 5 tan( y ) + 4 ln(z) = 5
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
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)+”.
(a) Estimate the value of tan(0.85) using a linear approximation. Let your point be a = use the fact that tan(x) = sec'(x)=- . Give the calculator value to 5 decimal dx cos? (x) places for comparison. (b) i. Give a reason that the function f(x x + x +5 has at least one zero. ii. Use the derivative to show that it cannot have more than one zero. Estimate the zero using 2 iterations of Newton's Method, if the...
1. For all x, the function f(x) = tan-',+ cot-1, has derivative f'(z)-12-17 0 1 +22 So f(x) must be a constant. a) What is that constant ? b) Explain by using a triangle c) What is limz+ */2-tan cot
Find the derivative. f(x)=ln (xe" + 9) f ,(x)= Find the derivative. f(x)=ln (xe" + 9) f ,(x)=