5. Find the derivative of each of the following: (a) (nz) 2 l (e) y-(tan)an o....
5. Find the derivative of each of the following: (a) y = (Inz) 2 l (e) y= (tan 2)tan . Find the equation of the tangent line to the curve 12-vin y = 9 at the point (3,1)
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?
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...
Given the function y = 4 - 2 sec x + tan x Find the equation of the tangent line to the curve at the point P(0,?).
Question 1. Compute the derivative of the following functions.(a) \(f(x)=x^{3}-\frac{2}{\sqrt{x}}+4\)(b) \(f(x)=2^{3 x-1}\)(c) \(f(x)=\ln \left(5 x^{2}+1\right)\)(d) \(f(x)=\frac{\tan (x)}{x^{2}+1}\)(e) \(f(x)=e^{x^{2}} \cdot \arctan (2 x)\)(f) \(f(x)=\sin (x)^{2} \cdot\left(\tan (x)+\cos (x)^{2}\right)\).Question 2. In geometry, the folium of Descartes is a curve given by the equation$$ x^{3}+y^{3}-3 a x y=0 $$Here, \(a\) is a constant.The curve was first proposed by Descartes in 1638 . Its claim to fame lies in an incident in the development of calculus. Descartes challenged Fermat to find the tangent line...
12. (5 points) (a): Find the directional derivative of f(x, y) = y² In r at P(1,4) in the direction of u = -3i + 3j. (b): Find the equation for the tangent plane and normal line to the surface cos(70) – z’y+e*2 + y2 = 4 at P(0,1,2).
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...
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
Problem 124: Study r = sin(a0) for 0-θく2π. Îfa E lo.5, 31 then which values of a give us a closed curve. I recommend using Desmos and the slider option to explore the graphs with technology. Problem 125: Find the polar form of the equation хуз-tan(y/x) 3. Problem 126: Find the equation of the tangent line to the curve r2 -3r +2 0 at the point
Problem 124: Study r = sin(a0) for 0-θく2π. Îfa E lo.5, 31 then which...
find d^2y/dx^2 for y=sec(x)
I l homework 3/8 Home-work-3: Problem 8 Previous Problem Problem List Next Problem (2 points) Find the equation of the line that is tangent to the curve 3. COS at the point (1, -31). The equation of this tangent line can be written in the form y = mx + b where n = and b Note: You can earn partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0...