Question

1. D/dx of 13xy?

2. d/dx of -y^2

Answer 1

The partial derivative of 13xy with respect to x is 13y, as y is held constant. The derivative of -y^2 with respect to x is 0 because -y^2 is considered as a constant in terms of x.

Step-by-step explanation:

Differentiation of Multivariable Functions

The differentiation of multivariable functions requires the application of partial derivatives. For the expression 13xy, we are interested in the partial derivative with respect to x, denoted as ∂/∂x. The differentiation rule for a product of two variables is applied, holding y constant since it is considered as a constant with respect to x.

For the first function, the derivative of 13xy with respect to x is:

1. Take the constant 13 out of the differentiation.
2. Differentiate x with respect to x, which is 1.
3. Multiply by the term y which is treated as a constant.

Therefore, D/dx of 13xy = 13y.

For the second function, since we are differentiating -y² with respect to x, and y is not a function of x (as implied by the question), the whole term is considered as a constant with respect to x. Thus, the derivative is zero:

D/dx of -y² = 0.

Answer 2

1. 13dxxy

2. -y^2dx

Step-by-step explanation:

Have a nice day! :)