Question

y=x sin x. Please Differentiate it (dx/dy).
❤
Please its Urgent​

Answer 1

This is a function which is in the form,

y = f(x)g(x)

It's the product of two functions and so we must make use of the product rule. This is a simple formula which you have to remember:

dy/dx = f'(x)g(x) + f(x)g'(x).

In words: the derivative of first function multiplied by the original second function, plus, the derivative of the second function multiplied by the original first function.

In this question,

f(x) = x

g(x) = sin(x)

so we can find that,

f'(x) = 1

g'(x) = cos(x)

and by substituting this into the formula for the product rule we get the answer:

dy/dx = sin(x) + xcos(x).

Answer 2

Heya!!

Product rule of Differentiation For two functions in product form.

Let F(x) be any function.

F(x) = u × v Where u and v are functions of x only.

It's Differentiation can be carried out by using product rule of Differentiation I,e

F'(x) = du/dx × v + dv/dx × u

y = x Sin x

Differentiate both sides w.r.t x we have

dy/dx = d(x)/dx × Sin x + x d(Sin x)/dx

dy/dx = 1 × Sin x + x × Cos x

dy/dx = Sin x + x Cos x

dy/dx = 1/(dx/dy)

dx/dy = 1/(dy/dx)

dx/dy = 1/{ Sin x + x Cos x }