If f(z) is analytic function expressed in polar form, show that: (sin + icos) of ᎧᎾ f'(z)=(cos- i sin () af Ər = r

Q: d 1 Use implicit differentiation to prove (arcsin a] %3D 1-a

A: The detailed solution is as follows below:

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point C.0. y =1- ... A…

A: Given; ey+cosx=1 at point (π/2,0).

Q: Assume that f and g are harmonic functions in R^n. Show that div(f ∇g − g∇f ) = 0.

A: Ans- We can start by computing the divergence of the vector field F = f∇g - g∇f:

Q: a) Prove that (arctan r 1+2 b) Using part(a), find the derivative of f (x)= arctan (208 )

A: Properties of derivative  f(g(x))=f'(g(x)) g'(x)ddxcosx=-sinxddxax=axloga

Q: (cos xy +5 dx + (1+ cos xy ) dy = 0 ху

A:

Q: If f(t) = 2 - 9t cos t find f'(0).

A: Given :ft=2-9tcost

Q: Find the derivatives of each of the following functions f(x)=-2 sinx b) y=-cos²x c) y = 3x sin x d)…

A: find the dervative

Q: Let f(z) = 4 cos I-3 tan z. %3D S(2) =D %3D

A:

Q: Which of the following is the tangent equation drawn to the pi/4 point on it? y = 25 - tanx curve…

A: This question is based on straight line. The general equation of a straight line is            y =…

Q: Find the tangent plane to the equation 2 = 4y cos(3x-5y) at the point (5, 3, 12). 2 =

A:

Q: +(x)=sin' (tan 3x) 1-

A: Since you have posted multiple questions, as per our policy we will answer first question. please…

Q: Show algebraically where the tangent line of the function r=1+cos theta is vertical and where the…

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Q: Find the slope of the tangent line to the polar curve r = 2 sin(36) at the point corresponding to =…

A: NOTE: Refresh your page if you can't see any equations. . substitute the given angel

Q: Determine the equation of the line tangent to y = (sin x)²(cos x) at the point (5,0).

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Q: Let f(x) = (8 sin z + 2 cos z)tan f'(z) -

A:

Q: omplex derivative of (Log z)^3

A: Given: log z3 To find: The complex derivative of given function.

Q: Now H= [² 2 id 2² H эрг = Ho 2² [Ho Sin (Kr_wt)] ar 2 [2 Ho Sin (Kr- wt) Ho 2/ [cos (kr-wt) x] K Ho…

A: They have derived the partial derivative. Our aim is to explain the derivative rule.

Q: +66 Next Page Previous Page xp 4) xp 3) xp O 2) xp Use implicit differentiation to find a if xy -…

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Q: Find the derivatives of inverse function: y = sec-1squareroot of 1 + x2 AND…

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Q: Suppose f"(x) =Osin(3z) and f'(0) 4 and f(0) =-2 f(T/3) = Note: Dont confuse radians and degrees

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Q: Find f' (x) : f(x) = V16 sin? x + 9 cos? x

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Q: f(x) = cos x + 3, [0, 27], midpoint

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