Question

What is the derivative of the function x^2 cos x

Answer 1

Answer:

u and v are functions of x,

u', v' are the derivatives of those functions

(uv)' is the derivative of the product.

The rule for products is (uv)'= u' v+ v'u

The first derivative of

x

2

is

2

x

The first derivative of

cos

x

is

−

sin

x

So (

x

2

cos

x

)'=

2

x

cos

x

−

sin

x

x

2

Or

2

x

cos

x

−

x

2

sin

x

Answer 2

Answer:

2xcosx-x²sinx

Step-by-step explanation:

Product rule states that;

d(uv)/dx = u'v+v'u

Let's , u=x² , u' =2x and v = cosx , v' = -sinx

So, dy/dx = d(x²cos)/dx

=> 2xcosx - sinx *x² Answer .

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