(c) The equation of a curve is given by, x²y² + 4y = x (i) Show that dy 1- 2xy? 4 + 2x²y | dx (ii) Find the gradient of the curve at (0,0). (iii) Hence, find the equation of the tangent to the curve at (0,0).

Q: g(x) = 1.1x + ex   , (0,1) Find an equation of the tangent line to the graph of the function at the…

A: Equation of tangent line when the slope and points are known: where x1 ,y1 represents the given…

Q: b) Use the definition of the derivative to find the derivative of f(x) = 4x³ + - at a = 1. 23

A: Given: fx=4x3+1x3; x=1 We know that ddxxn=nxn-1                                          ..1

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 1. у 3 ; d'y/dx

A: Question 1,Given,            y=x2-3x3xTo find : d3ydx3

Q: a) If a derivative of the function is given as: f'(x) = 9x² + 16x - 7 i) Find the function f(x) in…

A:

Q: Implicitly differentiate the equation y? + 4xy +x In 2x = 0. Isolate y' in the resulting equation.…

A: The equation of tangent on the curve f(x,y)= 0, at (a,b) is given by, (y - b) = y'|(a,b) (x - a)…

Q: Find the first and second derivatives of the function. g'(u) = g"(u) = g(u) = u(4u – 7)³ 1

A:

Q: a).y³ - 5y= 5x² + 7 point: (1,3)

A: According to the Bartleby guidelines we are supposed to do the first one of multiple questions…

Q: y=u (1+u³)* and u = (3x - 2)²

A:

Q: a) calculate the derivative of: f1(x) = 2x4 - 3x3 + ½x2 + 3 b) Calculate the equation of the line…

A:

Q: An implicit relationship between x and y is given by the equation x² + y² - 20x - 16y + 64 = 0. This…

A:

Q: (a) Find y'. (b) Verify that the point (0, 1) is on the graph of the equation. (c) Find the slope of…

A:

Q: b) y² + sin(y) = 2x6 point: (3,0)

A: Given that,(b) using implicit differentiation to find at the point

Q: Find the derivative of the function y = (4x + 5)°(5x + 1)~ª. dy dx II

A: For the solution of the problem follow the next step.