5. L 6. Let f(x) = lx2 - 91 GR a. Show that the function is not differentiable at x = +3. b. Find a formula for f'(x). c. Show that the graph of the function has corners at x = +3.

Q: If a is a positive integer, then the slope of the tangent to the graph of y = a²x – a ln(ax +1) at z…

A:

Q: If VT + Vy = 10 and the point (4, 64) is on the curve, find dy x=4 by implicit differentiation. dx…

A: Given that: x+y=10

Q: Find the value of the derivative y′(x) at x=0 for the function given by ey+xy=e.

A:

Q: 8) Suppose y log3(xy) = y² – 6x. 8.1) Find at (1,3) 8.2) Find the tangent line to the curve at (1,3)

A:

Q: If a is a positive integer, then the slope of the tangent to the graph of y = + a ln(ax) at x = 1 is…

A:

Q: ation: tanh’(x² + 3y 3

A: We have to find dydx of following equation. tanh3(x2+3y3)+ex2y4=3        ........(1)

Q: evaluated at x = 0.001 and y = 0.002 Compute the derivative of the following: 5 g(x) =, 2.1'x f(x) =…

A: topic - derivative of a function

Q: A) find the derivatives for the following: 1) y = In(In(sin¯'(e?r))) – 5-Inx 2) Y=sech-1(log, 93*) +…

A: Chain rule for differentiation: Let y=fghx then dydx=ddxfghx=dfghxdghx×dghxdhx×dhxdx Equation of…

Q: Q5: Find for the following functions: dx (4) y = x sinh 2x-cosh 2x (3) y = e* sin² x In√x

A: See this solution in below

Q: The tangent line to the graph of y = ln(2x) is perpendicular to a + 4y = 1 at the point where…

A: Given, The tangent line to the graph of y=ln(2x) is perpendicular to x+4y=1 Here, y=ln(2x) To find…

Q: Note that the solution of the DE: y(x) = e* (S e*~*dx +C) contains an anti derivative which has no…

A: Note: As there is not any point as d. So we cannot solve question h.. Here is the solution of f…

Q: If; of t = x then at t=1 is (Note that these functions in N) dx

A:

Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

A:

Q: dy y(ln y – In x +1) dx 1 C = -In None of the choices Option 1 1 C = -In C = -In- -ln Ontion3 Ontion…

A:

Q: Choose the right value of the following integral sie3f(=) f' (x) dx. where f is a continuous,…

A:

Q: dy Find for the following function: dx 1- y = etan'x 2- x³y + x²y = 2 at x = 2 3- y = log4(x³ – x)

A: Finding Derivatives by applying chain rule of derivative

Q: -1 The tangent line to the graph of y = tanh (4x) is parallel to z + y = 5 at point(s) where

A:

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: 1- for y= sech x is equal to: dx a) sech' x tanh x b) 3sech sech tanh x c)-3sech2x sechx tanhx

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Can you help me with this problem step by step?

A: Given that

Q: The graph of the function y = 3 sinh 4x has a relative maximum at a point O (0.0) O (0, 3) O (3.0)…

A:

Q: 17. For f(x) = x*, the instantaneous rate of change is known to be –32 at x = -2. Find the equation…

A: the given function is f(x) = x4 rate of change dydx=-32,          at x =-2

Q: 1. Calculate dy da for the following: (a) y ln(x + 2x³ - 6), =

A:

Q: An evolved kind of green fungi is shrinking at an initial rate following f(t) = vVE + 5, where t is…

A:

Q: B. Eind y' by implicit differentiation. Lesinh x+ Iny cosh x = tanh(x - y)

A:

Q: 35. Does the graph of Sx*sin(1/x), x + 0 f(x) (o. x = 0 have a tangent line at the origin? Give…

A: Given: fx=x2sin1x,x≠00,x=0

Q: Q2 find the derivative of the following: 1) y = 2sin?(5x) ,2) y = lnx'ncosh 5x ,3) xsin-14y = y…

A: See the attachment

Q: Find a nonzero value for the constant k that makes the function tan(kx) x < 0 f(x) = Зх + 2k?, x 2 0…

A:

Q: Q2) A: Compute at the point (1, 0) for the function dx S(x,y) = cot 1(4x + em(sin2xy)) + sinh(3) +…

A: Given that, f(x,y)=cot-14x+elnsin 2xy+sin h(3)+log2x2 Which can be re - written as,…

Q: II. Find dy/dx of the following functions: 4. ytan (tanh.x) 5. y=e³x sechx 6. y = √sech5x

A:

Q: Find an equation of the tangent line to the gra 26. 1+ln(xy) e (1, 1)

A: Obtain the derivative of the function with respect to x as follows.

Q: The derivative of y=eov? +cosh/x equals Select one: O y' = 2/x et +sinhx + sinh/x O None O y'=@ov +…

A: This is a composite function. Therefore we have to use rules for derivative of composite functions.

Q: 1.) The slope of the tangent line to the wve y?= 5+-1 at PCi,e) 2.) Find the First denivative of…

A: Using derivatives.

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = er+1) 3- xy +x*y = 3 at x = 1

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

A:

Q: What is (V | and find the relative minimum dx point as indicated by the black dot on the graph at…

A: Here we have ;  y=xx ..................(1) taking log both of sides

Q: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

A:

Q: 1. Find for differentiate each of the following functions. dy хр a) (In(coshx) sinh x) g) y = - b) y…

A: Given: a)lncoshx3c)y+4coshx2=exsin-1(2x)g)y=sinhxex

Q: Q2\A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Given that,

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + x²y 3 at x = 1

A: Here, We need to find the derivative of the given functions. To solve these questions, we need chain…

Q: S() dt, where f is a continuous function, find f(4). (c) A 10 ft ladder rests against a vertical…

A:

Q: The derivative of the function y = cos VI at z = is equal to 4

A:

Q: (3) (a) Find dy/dx by implicit differentiation and evaluate the derivative at the given point tan (x…

A: a) The equation given is tan(x + y) = x The point is (0, 0) Differentiate both sides with respect to…

Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

A:

Q: dy Find ck by implicit differentiation. √x+ y + √xy =4

A:

Q: 3 If the length of the curve y = 4 xž from the point (0, 0) to the point (xo, f(xo)) is L = ((20737)…

A: Given,          The length of the curve y=4x32 from the point 0,0 to the point x0,fx0           is…

Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: Find the length of the curve y = ln x from x = 1 to x = e.

A: Given:Find the length of the curve y = ln x from x = 1 to x = e.

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.