Q3. Find the indicated derivative(s).(a) g'(), where g(1) = S(x(1), y(1)). f(x, y) = x²y – sin y,x(1) = Vr² + 1, y(1) = e'ôgandduðv(b)where g(u, v) = f(x(u, v), y(u, v)). f(x. y) =xy - 4x2, x(u, v) = e, y(u, v) = J? + I sin u

Note the below results : Suppose gt=fx,y where x=xt and y=yt .Then according to chain rule…

Q3. Find the indicated derivative(s). (a) g(), where g(1) = f(x(1), y(1)), f(x, y) = x²y – sin y, x(1) = Vr +1, y(1) = e' %3D (b) and диду where g(u, v) = f(x(u, v), y(u, v)). f(x, y) xy-4x2, x(u, v) = e, y(u, v) J +I sinu

Q3. Find the indicated derivative(s). (a) g(), where g(1) = f(x(1), y(1)), f(x, y) = x²y – sin y, x(1) = Vr +1, y(1) = e' %3D (b) and диду where g(u, v) = f(x(u, v), y(u, v)). f(x, y) xy-4x2, x(u, v) = e, y(u, v) J +I sinu

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Q3. Find the indicated derivative(s).
(a) g'(), where g(1) = S(x(1), y(1)). f(x, y) = x²y – sin y,x(1) = Vr² + 1, y(1) = e'
ôg
and
duðv
(b)
where g(u, v) = f(x(u, v), y(u, v)). f(x. y) =xy - 4x2, x(u, v) = e, y(u, v) = J? + I sin u

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10. Use the Chain Rule to find the indicated partial derivative if F = Vu2 + v2 + w², u = xe, v = ye*, w = e*y, when x = 0 and y = 2
Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.
FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM ( 1. y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y =e^3x−e^−3x/e^3x+e^−3x 5. x =t/t−1, y =t2/t2−1

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ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated