Moving onto the right hand side, to differentiate 3xy we need to use the product rule, so we do the first product (3x) times the differential of the second (dy/dx) plus the second (y) times the differential of the first (3), giving 3x * dy/dx + 3y.

What is the derivative of XY?

And thus, your answer is xy’ + y.

What is the derivative of 3y?

Calculus Examples

Since 3y is constant with respect to x , the derivative of 3y with respect to x is 0 .

What is the differentiation of 0?

The derivative of 0 is 0. In general, we have the following rule for finding the derivative of a constant function, f(x) = a.

What is partial derivative of XY?

Using the chain rule with u = xy for the partial derivatives of cos(xy) ∂ ∂x cos(xy) = ∂ cos(u) ∂u ∂u ∂x = − sin(u)y = −y sin(xy) , ∂ ∂y cos(xy) = ∂ cos(u) ∂u ∂u ∂y = − sin(u)x = −x sin(xy) . Thus the partial derivatives of z = sin(x) cos(xy) are ∂z ∂x = cos(xy) cos(x) − y sin(x) sin(xy) , ∂z ∂y = −x sin(x) sin(xy) .

What is the derivative of 2x?

The derivative of 2x is equal to 2 as the formula for the derivative of a straight line function f(x) = ax + b is given by f'(x) = a, where a, b are real numbers. Differentiation of 2x is calculated using the formula d(ax+b)/dx = a.

What is the derivative of 4?

Since 4 is constant with respect to x , the derivative of 4 with respect to x is 0 .

What is the derivative of sinx?

The derivative of sin x is cos x. i.e., d/dx(sin x) = cos x.

ncG1vNJzZmivp6x7or%2FKZp2oql2esaatjZympmeUmr%2BqwsCtoK%2BdXaSzbn%2FXsmScoJWYuG6102amrqxdnbKzsYyhprBllKR6urvUZp2ippRiwamxjJ2cq6GmlsGqwsRmpp9lY63GcA%3D%3D