Question

f(x, y, z, t) = xy + zt + x2 yzt; x = k3 ; y = k2; z = k; t = VkFind df/dt at k = 1​

Answer 1

Answer:

$\frac{df}{dt}$ (t - 1 ) = 56

Step-by-step explanation:

From the above question,

They have given :

f(x, y, z, t) = xy + zt + x2 yzt;

            x = k3 ;

            y = k2;

            z = k;

            t = Vk

Here we have to find

df/dt at k = 1​

         X+Y+Z = 1

         2X+Y+4Z = K

         4X + Y + 10Z = K²

         2X+Y+4Z - ( X+Y+Z) = K - 1

          X + 3Z = K - 1

         4X + Y + 10Z - (2X+Y+4Z) = K² - K

         2X + 6Z = K (K - 1)

          2(X + 3Z) = K (K - 1)

         2(K - 1) = K (K - 1)

$\frac{df}{dt}$ = 4 * 5 + 3 * 12

$\frac{df}{dt}$ = 56

Hence, $\frac{df}{dt}$ (t - 1 ) = 56

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