Have a question about using WolframAlpha?Answer (1 of 6) I hope this helps corresponding elements are equal 2x − y = 10 3x y = 5 (1) Solving equations Adding (1) & (2) (2x – y) (3x y) = 10 5 2x – y 3x y = 15 2x 3x – y y = 15 5x 0 = 15 x = 15/5 x = 3 Putting value of x in (1) 2x – y = 10 2(3) – y = 10 6 – y = 10 –y = 10 – 6 –y = 4 y = –4 Hence, x = 3 & y = –4
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So,the 'y' in the question,arcsin(2x/1x^2) is a little difficult to handle,so a smart substitution has been done in the form of x=tan θ which simplifies the 'y' to be equal to 2 arctan(x) Now,y=2tan^1(x) Differentiating both sides,we get dy/dx=2*1/1x^2 as derivative of tan^1(x) is 1/1x^2 And dy/dx is what was asked in the question Cheers ) 133K views View upvotes 9 2 Related Ex 75, 6 Integrate the function (1 − 𝑥2)/(𝑥(1 − 2𝑥)) ∫1 (1 − 𝑥2)/(𝑥(1 − 2𝑥)) 𝑑𝑥= ∫1 (1 − 𝑥^2)/(𝑥 − 2𝑥^2 ) 𝑑𝑥Factor x^{2}2x1 In general, when x^{2}bxc is a perfect square, it can always be factored as \left(x\frac{b}{2}\right)^{2} \sqrt{\left(x1\right)^{2}}=\sqrt{2} Take the square root of both sides of the equation x1=\sqrt{2} x1=\sqrt{2} Simplify x=\sqrt{2}1 x=\sqrt{2}1 Subtract 1 from both sides of the equation x ^ 2 2x 1 = 0 Quadratic equations such as this one can be solved
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1 < x < 1 ← Prev Question Next Question → 1 vote 130k views asked in Mathematics by Afreen (307k points) Solve for x tan1 (2x/1x 2) cot1 (1x 2 /2x) = π/3;Piece of cake Unlock StepbyStep plot x^2y^2x Natural Language Math InputAnswer (1 of 12) Notice, \frac{x1}{2x1}\frac{2x1}{x1}=2 \frac{(x1)^2(2x1)^2}{(x1)(2x1)}=2 x^22x14x^24x1=2(x1)(2x1) 5x^22x2=4x^22x2 x^24x4=0
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