### Other calculators # Derivative of y=x^2sin(x)+2xcos(x)-2sin(x)

Function f() - derivative -N order at the point

from to

### The solution

You have entered [src]
 2
x *sin(x) + 2*x*cos(x) - 2*sin(x)
$$\left(x^{2} \sin{\left(x \right)} + 2 x \cos{\left(x \right)}\right) - 2 \sin{\left(x \right)}$$
Detail solution
1. Differentiate term by term:

1. Differentiate term by term:

1. Apply the product rule:

; to find :

1. Apply the power rule: goes to

; to find :

1. The derivative of sine is cosine:

The result is:

2. Apply the product rule:

; to find :

1. The derivative of a constant times a function is the constant times the derivative of the function.

1. Apply the power rule: goes to

So, the result is:

; to find :

1. The derivative of cosine is negative sine:

The result is:

The result is:

2. The derivative of a constant times a function is the constant times the derivative of the function.

1. The derivative of sine is cosine:

So, the result is:

The result is:

The graph
The first derivative [src]
 2
x *cos(x)
$$x^{2} \cos{\left(x \right)}$$
The second derivative [src]
x*(2*cos(x) - x*sin(x))
$$x \left(- x \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right)$$
The third derivative [src]
            2
2*cos(x) - x *cos(x) - 4*x*sin(x)
$$- x^{2} \cos{\left(x \right)} - 4 x \sin{\left(x \right)} + 2 \cos{\left(x \right)}$$
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