Question 18 Let z = z(u, v, t) and u = u(x, y), v = v(x, y),...

Question 18 Let $z = z(u, v, t)$ and $u = u(x, y)$, $v = v(x, y)$, $x = x(t, s)$, and $y = y(s)$. The expression for $\frac{\partial z}{\partial t}$, as given by the chain rule, has how many terms? Three terms Four terms Five terms Six terms Seven terms Nine terms None of the above

Transcript

00:01 In the question, we have to first define the chain rule.

00:07 So note that if f and g are the differentiable function, if f and g both differentiable function, and f of x is the composite function which is defined by f of x is equal to f of g of g of g of then f is differentiable and f -dash is given by the product that is f -dash -of -s is equal to f -dash -of -x times derivative of g of x so by using the chain rule we will first find the derivative of f of x is equal to f -of -x is equal to e to the power 2x.

01:18 So differentiating it, we get f -dash -of -x is equal to derivative of e to the power 2x.

01:28 That is we have f -dash of x is equal to e to the power 2x times derivative of 2 times x.

01:36 So we have f -dash of x is equal to e to the power 2x times 2, which is a required derivative by using the chandroth.

01:47 Next we have to find the derivative of function f of x which is given as log of 2 times x squared plus 4.

01:57 So we have f dash of x derivative of log of 2x square plus 4 will be 1 over 2x square plus 4.

02:07 Then we have to take the derivative of 2 times x square plus 4.

02:11 Therefore we have f -dash of x is equal to 4 times x over 2 times x squared plus 4, which is a required answer for the second function.

02:25 Now in the third, we have to find the derivative of function f of x is equal to quart of 3 times x square.

02:34 Note that the derivative of 4x is equal to negative cosec square x...

Question

Question 18 Let $z = z(u, v, t)$ and $u = u(x, y)$, $v = v(x, y)$, $x = x(t, s)$, and $y = y(s)$. The expression for $\frac{\partial z}{\partial t}$, as given by the chain rule, has how many terms? Three terms Four terms Five terms Six terms Seven terms Nine terms None of the above

Please give Ace some feedback