4. Use definition (not tables) of L {f(t)}= [ e"f(t)dt to find L{sin(2t)} . %3D

Q: 9 tan t Find the derivative of the function y = 2 + 2 sect dy dt

A: Explanation and solutions is given below....

Q: Q2) A: Compute 2 at the point (1, 0) for the function dx S(x.y) = cot(4x + eln(sinzxy)) + sinh(3) +…

A: Consider the given function. f(x,y)=cot-1(4x+ein(sin2xy))+sinh(3)+log2x2

Q: Find th epwation of the tangent line to An- (x-2y): 2xy-1 at print (1, 2) d [sin- (x-2g)] = (2xy-1)…

A:

Q: In the given question/s, find dy /dx by implicit differentiation :-   y = sin xy

A: Given expression: y=sinxy

Q: Find the indicated derivative: d/dt ((e^t ,e^(2t),e^(3t)) X (sin(t),cos(t),tan(t)) )

A: We have to Find the indicated derivative of ((e^t ,e^(2t),e^(3t))(sin(t),cos(t),tan(t)) )

Q: 4.62. Evaluate the derivative of the Gamma function and see dT'(x) r'(x) = dx ' (In t)e"'dt

A: To differentiate the gamma function:         Γ(x) = ∫0∞tx-1e-tdt Integral definition of gamma…

Q: dy соmpute dx for implicitly given function cos(xy) + 2y = x³

A: cos(xy)+2y=x3Differentiate with respect to x,-(sin(xy))y+xddx(y)+2ddxy=3x2

Q: 1) Find dy/dr by implicit differentiation. tan n'(xy"+y)= x

A:

Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: Solve th D.E using Exact dx +(x² +3y* )dy

A:

Q: Find the derivative of y with respect to t at t=2 if a) у %3D х + sinх - cos(1 + x+x?) аnd x = (t/t…

A:

Q: B- Find dy / dx for the following functions: (3 mark) * 1- Y= sin( coshx log, 2 ) 1 Add file 2- (3…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Solve for the following implicit derivative: d²y si sen(y) = ycos(2x) dx?

A: We have to find the double derivative of the given function.

Q: In the given question/s, find dy /dx by implicit differentiation :-   x2 - y2 =25

A: Given: x2-y2=25 To Find: dydx by implicit differentiation

Q: . Suppose y is a function of x defined implicitly by sin y + y = x²y² + In(x) – 1 Find dy/dx and…

A:

Q: At time t = 0, then th

A: P(t)=0.5t4-16t3+144t2       , 0≤t≤12At t=0 the sale begins,costco is having a 12 hour sale,The rate…

Q: In the given question/s, find dy /dx by implicit differentiation :-   x2 + y2 = 9

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

A:

Q: Find dy/dx by implicit differentiation for the following.

A: Given expression: 5y2=4x-34x+3

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

A:

Q: (a) Find the differential dy. y = cos(x)

A: Differentiate the given function with respect to 'x' and find 'dy'.

Q: 9. Find dy/dx by implicit differentiation of y? = In(x), at (e36,6).

A:

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

A:

Q: 1. Solve for y of the Separable D.E. sinx dx +y dy = 0

A: To solve the given differential equation for y.

Q: Q1: Find 1) e (3 + e6t)2 2) l {e-3t(t + 1)²} t } 3) e- sin 3x dx dt 0,

A:

Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: Find the differential dy of the given function. dy sec x x² +9

A:

Q: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: 4. The given equation sinh(xyz) = x+ y + 3z implicitly defines a differen- dz Find ax tiable z as a…

A: Differentiate of sinh(x) =cosh(x)

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: t. ト ニ

A: We can solve them to find dy/dx as below

Q: Let e 2* = 2 find dy dx at x = 1

A:

Q: Find the differential dy of the given function.    y = x tan x

A:

Q: Evaluate the second derivative of mq4.5.png os (bVx³) f(x) = a ln sin(cx2) if a = 21, b = 0.5, and c…

A: Given that, f(x)=alncosbx3sincx2a=21, b=0.5, c=5Substituting the values of a, b and c, we…

Q: Find dy/dx of the function below. 2x³ + e^(2y) = cos3y

A: 2x3+e2y=cos(3y)Differentiate with respect to…

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x2 – 6xy + y3 = 24

A:

Q: What is the first derivative of s(r) = log, sin z 712+8z+2 Provide your answer below: s'(x) =]

A:

Q: The of the function y= e sin(3x)- In(5.x +2x+1) dx at (0,0) is: А. О В. -1 С. 1 D. 3

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: 2. 2メ dy dx for y = Cos (ln x + e put lに

A: y = cos2(ln(x) + e2x)

Q: (c) Find dy/dx by implicit differentiation cos(x² y) = x

A: We are given, cos(x2y) = x We need to find dy/dx

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: ydx -( x+***ty? dy = 0

A:

Q: Find the differential dy of the given function. (LUse "cx" for dx.) x +3 3x

A: We will solve the problem

Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

A:

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: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

A:

Q: Find the indicated derivative: d/dt ( (t^3 +3, 3t^2 -4)* (tan(t),sin(t)) )

A: We have to Find the derivative of d/dt ( (t^3 +3, 3t^2 -4)* (tan(t),sin(t)) )

Q: 3. Evaluate the following derivatives: a) y = In[sinh(2x)] b) f(t) = tanh-1 VE

A: Derivative of the inverse hyperbolic function formula: -  ddx(sinhx)=coshx ddxtanh1x=12ln1+x1-x…