if x < 0 (b) f(x) = lx² _if x > 0 f' _(0) f',(0) Is f differentiable at 0? Yes No

Q: S In(sin(x))dx

A: Given, I=∫lnsinx dx To evaluate I.

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: The solution for the above question is as shown below.

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

A: i) The given function is fx=sin2x. Given that the domain of the function is 0,π. Obtain the first…

Q: dy Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y³. dx

A: Given that: 3x2 +2xy = -4y3. Find dy/dx. We know that derivative of xn is nxn-1.   Here i attached…

Q: The deferential of point functions are exact differentials. Select one: True False

A: True

Q: Find the derivative: y = ln² (3x + 1) O y' = O O O y' = y' = y = 2 ln(3x + 1) (3x + 1) 6 (3x + 1) 3…

A: Consider the function y=ln2(3x+1). The objective is to find the derivative of the function.

Q: If x+y divided by x-y= x^2+y^2 and dx/dt=12, then what is dy/dt when x=1 and y=0? show all work…

A: Given thatx+yx-y=x2+y2x+y=(x-y)(x2+y2)  [cross multiply]x+y=x3+xy2-x2y-y3

Q: what is higher order partial derivative and total differentials?

A: We have to define given Terms.

Q: 4. Find by implicit differentiation of x sin(y) = y cos (x) dx

A: The given problem is solved below in detail.

Q: Determine the second derivative of f (x)= x 'e* at x = -2 with a step-size of h=0.50 using Central…

A: We have to find the second derivative of the following function at x=-2 with step size h=0.5 using…

Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: ) y = In³ )) (tanh²(scc '(x²)

A:

Q: Use forward, backward and central difference to estimate the first derivative of f (x) = In at x =…

A: Given function is fx=lnx and x=3 Step size h=0.01 We have to estimate the first derivative of fx=lnx…

Q: f) 3rd derivative of y : sin 3x g) Find if yVx – 8 = xy +2. if yvx – 8 = xy + 2. dx

A: Note: As in questions d and e no instruction is given solved f and g for you.

Q: (A) Ln(2) S Sinh(x) Cosh² (x) dx

A:

Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: Find the anti-derivative: x2/3 dx. Upload Choose a File

A: Using simple integration method to solve the question.    Attached below is the detailed solution.

Q: d arctan (tanh x) dx Show that sech 2.x.

A:

Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

Q: find derivative       1. y = ln 3x + x    2. y = ln (t2)    3. y = ln (3/ x)    4. y = ln (u + 1) -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Differentiate f(x) = sinh (x) + 2 cosh (x) - sech (x)

A: Aim: We have to differentiate given function.

Q: (b) Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y3. dx

A:

Q: ion ƒ(x) is infinitely differentiable and that f'(x) = - st, second, third and n-th derivative of f…

A:

Q: Find the derivative of y = 4) G* eln sin-) y = G (In-x) sin + V4 – x2. x sin¬1 In sin + (Tx-1 1 y' =…

A:

Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

A:

Q: Plot f (x) = ln x − 5 sin x on [0.1, 2] and approximate both the critical points and the extreme…

A:

Q: Compute Anti-Derivative (-1 --> 1)  (x^3 + x) / (cos(x) + pi) dx

A:

Q: If f(x) is odd function, then the derivative of y=sinh (f (-x)) equals Select one: o y'=Xf'x) – f x)…

A: Differentiate wrt x

Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

Q: Find both first partial derivative Z = 15x x/y az az ду

A: As we know that: The the Power law: ddxxn=nxn-1 From the given problem: z=15xy

Q: rIn 2 cosh x dx. Vsinh a x + 4 sinh x +2

A:

Q: 8. The value of f sinh* x cosh³ x dx

A:

Q: Calculate the partial derivative * using implicit differentiation of exy + sin (3xz) + 2y = 0. (Use…

A:

Q: What is the second derivative of ecON (), , Cosh (A sinh?(x)e cosh (x) + cosh2(x)ecosh («) B sinh…

A: Let the given function is y=ecosh(x).

Q: find derivative 1. y = 1/( ln 3x)      2. y = ln (t3/2) + sqrt(t)    3. y = ln (sin x)      4. y =…

A: Hi! Your question contains many sub-parts. As per norms we will be solving only 3 sub-parts. Since…

Q: 2. Use central difference approximations to estimate the first and second derivatives of y = e* at x…

A:

Q: Find cosh æ In(sinh x)dx.

A:

Q: Find:  ∫cosh^4 (x) sinh^5 (x) dx.

A:

Q: 1 3), sinh(x)-cosh(x) dx

A:

Q: (1+sin2x)^1/x lim x approaches 0   So far I have broken it down to (ln(1+sin2x))/x and did the…

A: Let y= (1+sin2x)^(1/x)Then take ln on both sides.

Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

A:

Q: Find the first derivative of * In (sec y + tan y) - x - sinx = 2 O tany (cos.x + 1) O cos y (cos x +…

A:

Q: Find dy ax oy Impticit dipTErentation 3. Find 2nd derivative

A: 1) The given equation is 2x2+2y2=17 Differentiate both sides of given equation 2x2+2y2=17 with…

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

A:

Q: The second derivative of an anti-derivative of a differentiable function F R-R is: O possibly…

A: The second derivative of an anti-derivative of a differentiable function f:R→R is

Q: limit x approaches zero, sin^2x/x

A: Given,

Q: 3. SIX f- - dx x in x√√(inx)2-9

A:

Q: 8. Scoth 2x In (sinh 2x) dx

A:

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.