Question

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Answer 1

Answer:hope it helps u

Step-by-step explanation:

(i) xSinx

We apply d(uv)/dx here

d(uv)/dx=u (dv/dx)+v(du/dx)

Here u=x and v=Since

Therefore,

d{xSinx}/dx=x{d(Sinx/dx)}+Sinx{dx/dx}

=xCosx+Sinx(1)

=xCosx+Sinx

This is the answer...

(ii)x^4+Cosx

=d{x^4}/dx+d{Cosx}/dx

=4x^3-Sinx

Since d{x^n}/dx=n{x^(n-1)} & d{Cosx}/dx= -Sinx

(iii) x/Sinx

It is in the form of (u/v)

We know, d(u/v)=[v{du/dx}-u{dv/dx}] / v^2

Therefore,

d{x/Sinx}/dx=[Sinx{dx/dx}-x{d(Sinx)/dx}]/ Sin^2(x)

=[Sinx(1)-x(Cosx)]/Sin^2(x)

=(Sinx-xCosx)/Sin^2x

={Sinx/Sin^2x}-{xCosx/Sin^2x}

={1/Sinx}-{xCosx/Sin^2x}

This is the answer.

Note that the third answer given in your notebook is wrong.There should be minus sign instead of plus sign in final answer.