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P rov et h a t d/(dx){x/2sqrt(a^2-x^2)+(...

`P rov et h a t d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a) }=sqrt(a^2-x^2)`

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Prove that d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)}=sqrt(a^2-x^2)

Prove that d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)}=sqrt(a^2-x^2)

Prove that: d/(dx)[x/2\ sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)]=sqrt(a^2-x^2)

Differentiate the following w.r.t.x. (sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)-x^(2))-sqrt(a^(2)-x^(2)))

Differentiate tan^(-1)(x/(sqrt(1-x^2))) with respect to sin^(-1)(2xsqrt(1-x^2)), if -1/(sqrt(2)) < x< 1 /(sqrt(2))

Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to tan^(-1)(x/(sqrt(1-x^2))) .

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t. tan^(-1) ((x)/(sqrt(1-x^(2)))) .

If x in((1)/(sqrt2)1). Differentiate tan^(-1)(sqrt(1-x^(2))/(x)) w.r. t. cos^(-1)(2xsqrt(1-x^(2))).

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

If x in (0,pi/2),t h e ns howt h a t d/(dx)cos^(-1){7/2(1+cos2x)+(sqrt(sin^2x-48cos^2x))sinx} =1+(7sinx)/sqrt(sin^2-48cos^2x)

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
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  2. If y=sqrt(x)+1/(sqrt(x)),p rov et h a t2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

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  3. P rov et h a t d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a) }=sqrt(a^2...

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  4. If x y=4,p rov et h a tx((dy)/(dx)+y^2)=3y

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