Final answer:
The differentiation of the equation 3x² + 4y = 10 with respect to t, assuming x and y are functions of t, yields 6x(dx/dt) + 4(dy/dt) = 0. Comparing with the options, the correct answer is (b) 6x + 4(dy/dt) = 0.
Step-by-step explanation:
To differentiate the given equation 3x² + 4y = 10 with respect to t, it is assumed that both x and y are functions of t. Therefore, the derivatives of x and y with respect to t will be considered.
Differentiating each term of the equation separately with respect to t, we get:
- The derivative of 3x² with respect to t is 6x(dx/dt) because of the chain rule.
- The derivative of 4y with respect to t is 4(dy/dt), again because of the chain rule.
- The derivative of a constant, 10, with respect to t is 0.
Putting it all together, we get 6x(dx/dt) + 4(dy/dt) = 0.
If we're looking for a direct comparison with the answer options provided and assuming dx/dt is simply represented as x', then the differentiated equation resembles option (b): 6x + 4(dy/dt) = 0.