If f(x) = 3 x2 +x , then f'(1+h) –f'(1) is limn→0 h DNE none

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

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Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: Solve Cauchy Euler DE 4x^2y"-4xy'+3y=sin ln(-x), x less than 0

A: Let t =-x >0. Then the differential equation       4x2y''-4xy'+3y=sinln-x becomes…

Q: Find the derivative of y 16 In (In(6x)). (Use symbolic notation and fractions where needed.) dy dx…

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Q: Compute dy/dx for the function. y = sinh 2 8x O 2 sinh 8x cosh 8x O 2 cosh 8x 16 sinh 8x cosh 8x 16…

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Q: 'the line tangent to the graph of y= In(3x) + 2x e at x=1 6 Jx-1 by using quotient rule. Vx +1 for…

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Q: Suppose f(x) = df Find the derivative dx In(In(In(In(x)))). f' (x) :

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Q: Verify the homogeneity of the differential dy _ y²-2xy x2 - 2xy dx

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Q: 5. Calculate the derivatives of sinh¬1x, cosh¬1 x, and tanh¬ x. Hence, express each of the…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

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Q: Vz²+1 ev° dy In a

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Q: limit x to 0 sin(4t)sec(1000t)/10t

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Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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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 the derivative of the function by the limit process. h(s) = −2 (square root of x)

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Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: Find dy/dx for x⁴+siny=x³y²

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Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: - ((x3 + x)sech(In x)) = dx EX)-

A: To find  ddx(x3+x)(sech(ln x) We use product rule  d(uv)=udv+vdu Let  u=x3+x,     v=sech(ln…

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: Find the derivative of y with respect to X. y = tan 1 5x 105x(1 + 5x) 2(1 + 5x/5x J1- 5x 1+ 5x

A: It is derivative.

Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: Determine the indicated (in the attached image) partial derivative of z = x4y5 - cos(x3y2)

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Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

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Q: 5. Find where y = In(cosh(2x)) + /sinh-1(2x) + tanh² (7x). dy dx

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Q: Find the derivative of y(x) = In (8(In(x))'). (Use symbolic notation and fractions where needed.) dy…

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Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

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Q: 57 ves y sinx and y=cosx from x=- to x=- 4 4

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Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

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Q: Ay Find the derivative of the following using lim Ax-0 Ar %3D dx ala

A: Part (a) - y = 4x2-5x       ...........(1)Given that,dydx = limx→0 ∆y∆x We can write it as - dydx =…

Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

Q: find dy/dx of y=sin^2 4x+1/2 cos 8x

A: Given,         y=sin24x+12cos8x

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

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…

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Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

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Q: show that the lim dose not exist x.y-00

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Q: Limit 0 to 2 √x dx

A: We have to find the definite integration: ∫02xdx We know the formula of integration, ∫xndx=xn+1n+1+C…

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: 5. Find by implicit differentiation for x + y = xy. dx

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Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…