Question

defrentiation
y=x3sinx​

Answer 1

Step-by-step explanation:

are differentiating a product (two things times together) we can use the product rule which is if:

y = u(x)v(x)

then

dy/dx = u(dv/dx) + v(du/dx).

So firstly looking at our equation we need to identify u(x) and v(x). In our case

u(x) = x3 and v(x) = sinx

Now we need to differentiate both of them seperatly so (remember when we differentiate we times by the old power and then subtract a power)

du/dx = 3x2 and dv/dx = cosx

Now putting all this into the formula we have

dy/dx = u(dv/dx) + v(du/dx)

= x3cosx + sinx(3x2)

Then rearranging this we get

dy/dx = x3cosx + 3x2sinx

Answer 2

Answer:

dy/dx=d(x3sinx)/dx

= 3x2 cosx