Question

y= x^2 sinx / x + cosx find deviation of the function
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Answer 1

Step-by-step explanation:

If you are studying maths, then you should learn the Product Rule for Differentiation, and practice how to use it:

ddx(uv)=udvdx+dudxv, or, (uv)'

=(du)v+u(dv)

I was taught to remember the rule in words; "The first times the derivative of the second plus the derivative of the first times the second ".

This can be extended to three products:

ddx(uvw)

=uvdwdx+udvdxw+dudxvw

So with f(x)=x2

sinx+xcosx

we will need to apply the product rule twice;

For the first component Let y

=x2sinx {Let u

=x2

==⇒ dudx=2xAnd v

=sinx

==⇒ dvdx

=cosx ddx(uv)

=udvdx+dudxv

∴ddx(x2sinx)

=(x2)(cosx)+(2x)(sinx)

∴ddx(x2sinx)=x2cosx+2xsinx ..... [1]

For the second component Let

y=xcosx{Let u=x

==⇒ dudx=1

And v=cosx

==⇒ dvdx=

sinx ddx(uv)=udvdx+dudxv

∴ddx(xcosx)=(x)(−sinx)+(1)(cosx)

∴ddx(xcosx)=cos x−x sinx ..... [2]

Combining the results [1] ad [2] we get;

dydx=x2cosx+2xsinx+cosx−xsinx

∴dydx=x2cosx+xsinx+cosx

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Answer 2

Step-by-step explanation:

the denomeretor Will be multiplies with 3

so answer is 1/162