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Differentiate (x cos x)^(x)+(x sin x)^(1...

Differentiate `(x cos x)^(x)+(x sin x)^(1//x)` with respect to x.

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The correct Answer is:
`dy/dx=(x cos x)^(x)[-x tanx+1+log(xcosx)]+(x sin x)^(1//x)[1/x cot x+1/x^(2)-1/x^(2)log(x sin x)]`
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SUNSTAR PUBLICATION-P.U .BOARD LATEST MODEL QUESTION PAPER - 2 -PART-C
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  2. Find dy/dx if x^(3)+x^(2)y+xy^(2)+y^(3)=81

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  3. Differentiate (x cos x)^(x)+(x sin x)^(1//x) with respect to x.

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  4. Find the absolute maximum value and the absolute minimum value of the ...

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  5. Find int(xe^(x))/((1+x)^(2))dx

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  6. Evaluate: int2/((1-x)(1+x^(2)))dx

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  7. Find the area bounded by the the curve y=cos x between x=0 and x=2pi.

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  8. Find the general solution of dy/dx+y=1(y!=1)

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  9. Find the value of p so that the lines (1-x)/3=(7y-14)/(2p)=(z-3)/2 and...

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  10. Find the area of the rectangle having vertices A,B,C and D with positi...

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  11. Show that four points A,B,C and D with position vectors4i+5j+k,-(j+k),...

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  12. In answering a question on a multiple choice test a student either kno...

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  13. If f:ArarrA defined by f(x)=(4x+3)/(6x-4) where A=R-{2/3}, show that f...

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  14. If A=((1,1,-1),(2,0,3),(3,-1,2)),B=[(1,3),(0,2),(-1,4)] and C=[(1,2,3,...

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  15. Solve by matrix method: 4x+3y+2z=60, x+2y+3z=45, 6x+2y+3z=70

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  16. If y=3 cos(log x)+4sin(logx) show that x^(2)y(2)+xy(1)+y=0

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  17. A ladder 5cm long is leaning against a wall. The bottom of the ladder ...

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  18. Find the integral of sqrt(x^(2)-a^(2) with respect to x.

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  19. Find the area of the smaller region enclosed by the circle x^(2)+y^(2)...

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  20. Solve the differential equation dy/dx+2y tan x=sin x,y=0 when x=pi/3

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