If t=√x+4, then ((d x)/(d t))ₜ₌₄ is :

Solution

Physics sir · 3 steps

Get x on its own as a function of t first, then differentiate. The 4 inside the bracket does the work.

1. Make x the subject. From t = √x + 4 we get √x = t - 4. Squaring both sides gives x = (t-4)².
2. Differentiate. Use the chain rule on the square. The derivative of the inside, t - 4, is 1.

   dx/dt = 2(t-4)

3. So. At t = 4, dx/dt = 2(4-4) = 0. The answer is zero, option (b).

The idea to keep. To find dx/dt, write x as a function of t first, then differentiate. Put in the given value only after you have differentiated.

Answer from the NTA final answer key. Solution by PrepWiser.