42. 1 B. arccosh x x Va² + x² 1 43. С. | —arccoth x x Va² – x² 1 - 44. D. -arccsch x Va2 + x2 45. 1 E. -arcsech x -2

Q: 3. f(x, y) = (3x - 5y)2 + e4x In(4y – 9) + %3D 135 x4

A: We know, ddxxn=nx(n-1)  , for any real number n. ddxln(x)=1x

Q: the equation ariables x and y and

A:

Q: _x²+y? f (x,y) = e' 3 (sin(x²) + cos(y²)) %3D %3D 3

A: Given function  fx,y=e-x2+y23sinx2+cosy2 fx=e-x2+y232xcosx2+sinx2+cosy2-2x3e-x2+y23…

Q: Find the derivative of y = 2 + v2 + vx5 |2 + V2 + Vx5

A:

Q: Is it possible to evaluate the anti-derivative below? | (x + 1) cOS (2x) cos (x2) dx

A:

Q: Compute the derivative of y= [(x+1)/x^3-1)]^1/2

A: The given function is y=x+1x3-112. Obtain the derivative as follows.

Q: the directional d + 3y2 + 5z² at pa

A:

Q: Evaluate the following derivative d/dt (at^2+bt+K)

A:

Q: To compute fxyz, we first take the partial derivative with respect to which variable?

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Q: Which derivative rule is used to derive the Integration by Parts formula?

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Q: Find the derivative of 1-3)* (t3 -8) ,t # 2 2-t

A: Explanation of the answer is as follows

Q: Determine the directional derivative of X²Yz +4XZ² at the point P(1,-2,1) in direction a=2û - j +² R…

A:

Q: 2x f(x) sec(t*) dt. %3D -2x

A: Given,            f(x) =∫-2x2xsect4 dt

Q: Find the first and second derivative if w = 3z-2-(1/z)

A:

Q: Find the anti-derivative of

A: Answer and explanation is given below

Q: What

A: The correct option is (B).

Q: 음고+ 음 + 2V- e The first derivative of y = 3x5 is %3D

A: Recall: dxndx=nxn-1 dc1f(x)±c2g(x)dx=c1df(x)dx±c2d[g(x)]dx ; where c1 and c2 are constants.…

Q: A particle’s velocity is given (in units of meters per second) by the function v = 1 + (t^3)/10 –…

A: A particle’s velocity is given (in units of meters per second) by the function…

Q: Find the derivative 3a+bt3 2b f(t) =+ V6at6. 5 3t

A:

Q: Suppose velocity of a car starting from rest is modelled by equation V(t)= In(4t^3 + 1) m/s What…

A: