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Write down expressions for the first-order partial derivatives, ?z and ?z for ?x ?y (a)z=x2 +4y5...

Write down expressions for the first-order partial derivatives, ?z and ?z for ?x ?y (a)z=x2 +4y5 (b)z=3x3 ?2ey (c)z=xy+6y (d)z=x6y2 +5y3

Expert Solution

a.

z = x^2 + 4y^5

(dz/dx) = Partial derivative of z with respect to x

= 2x ^(2 – 1) + 0

= 2x [Answer]

z = x^2 + 4y^5

(dz/dy) = Partial derivative of z with respect to y

= 0 + (4 × 5) y ^(5 – 1)

= 20y^4 [Answer]

c.

z = xy + 6y

(dz/dx) = Partial derivative of z with respect to x

= y × x ^(1 – 1) + 0

= y × x ^0

= y × 1

= y [Answer]

z = xy + 6y

(dz/dy) = Partial derivative of z with respect to y

= x × y^(1 – 1) + 6y^(1 -1)

= x × y^0 + 6y^0

= x × 1 + 6 × 1

= x + 6 [Answer]

d.

z = x6y^2 + 5y^3

(dz/dx) = Partial derivative of z with respect to x

= (6y^2) × x ^(1 – 1) + 0

= (6y^2) × x ^0

= (6y^2) × 1

= 6y^2 [Answer]

z = x6y^2 + 5y^3

(dz/dy) = Partial derivative of z with respect to y

= x(6 × 2)y^(2 -1) + (5 × 3)y^(3 – 1)

= 12xy + 15y^2 [Answer]

Rahul Sunny answered 1 year ago

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Question

Write down expressions for the first-order partial derivatives, ?z and ?z for ?x ?y (a)z=x2 +4y5...

Solutions

Expert Solution

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