(4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u = e dy du

Q: 12 3. (sin x)y' +y cos r = r sin a,

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Q: dy 3YUse implicit differentiation to find y or a) 2x +v° =7x² -6 b) x +xy=y +15

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Q: F(x) = 1+e siny x %3D -- = -15 e sin4X- se"co54X fca) = fco) = -8 R fくり) = fci-2) = 4.2398 > KMS %3D…

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Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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Q: Find f. f(t) = f"(t) = 7et + 3 sin t, Need Help? Read It f(0) = 0, f(π) = 0

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Q: Find the derivative of y = In O O a.) dy dx =In(5) +4ln(x) —In(cosx) 4 1 dx X COSX b.) dy = c.) dy 1…

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Q: Q2) Find az/du and äz/au for the following function and then find dz/ou and az/dv at the given…

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Q: 04) Find dy /dx for the following functions: a) y².cotx= [sin(x.y)]-¹ b) y = (lnx + x)tan

A: See the answer below

Q: #15) Determine y' a.y=sin 2x b. y = x² sinx co y = sin(-x) Determine #16.> d.) y = cos x sin x e-> y…

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Q: 5-find Аху : xe 12) if f(x, y) = xe

A: First I have mentioned what we have to find then just use the rule of partial derivative find the…

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: nd r'(t), r"(t), and r'(t) · r"(t). r(t) = 4 cos(t)i + 3 sin(t)j a) r'(t) b) r"(t)

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Q: Calculate dwldu and using the following functions: = f(x, y, z) = 3x2 – 2xy + 4z2 x(u, v) = e" sin v…

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Q: Q NO3)IF y=Jsinx + Vsinx + Vsinx + . then show that(2y-1) = cosx .And Also Find dx (5vcosx) dx

A: Our objective is to find the derivative of above functions.

Q: y = u²+1, uzt + 3t ) t=2x1 what's dy dx for x=1?

A: The given functions,.We have to find for .

Q: dy b) Find dx Y=cot4 (sinx) XU

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Q: b.9f Fex)=x Sin lgix), where gL1)= , and g' (1)= -1, then f'(1)=2

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Q: How did he get the second derivative step by step and a clear line please 3 F(x) = 1+e siny x Fex)…

A: Let fx=1+e-xsin 4x