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14. If (xsqrt{1+y}+ysqrt{1+x}=0), for (-1<x<1), prove that (frac{dy}{dx}=-frac{1}{left(1+xright)^2}). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11. 1. (left(3x^2-9x+5right)^9). 2. ({sin}^3{x}+{cos}^6{x}). 3. (left(5xright)^{3cos{2}x}). 4. ({sin}^{-1}{left(xsqrt…

13. Find (frac{dy}{dx}), If (y={sin}^{-1}{x}+{sin}^{-1}{sqrt{1-x^2}}),(-1le xle1). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11. 1. (left(3x^2-9x+5right)^9). 2. ({sin}^3{x}+{cos}^6{x}). 3. (left(5xright)^{3cos{2}x}). 4. ({sin}^{-1}{left(xsqrt xright)}),(0le xle1).…

12. Find (frac{dy}{dx}), if (y=12left(1-cos{t}right)),(x=10left(t-sin{t}right)),(-frac{pi}{2}<t<frac{pi}{2}).   Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11. 1. (left(3x^2-9x+5right)^9). 2. ({sin}^3{x}+{cos}^6{x}). 3. (left(5xright)^{3cos{2}x}). 4. ({sin}^{-1}{left(xsqrt xright)}),(0le xle1).…

Differentiate w.r.t. x the function in Exercises 1 to 11. 11. (x^{x^2-3}+left(x-3right)^{x^2}), for x>3.     Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11.…

Differentiate w.r.t. x the function in Exercises 1 to 11. 10. (x^x+x^a+a^x+a^a), for some fixed a>0 and x>0.   Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises…

Differentiate w.r.t. x the function in Exercises 1 to 11. 9. (left(sin{x}-cos{x}right)^{left(sin{x}-cos{x}right)}), (frac{pi}{4}<x<frac{3pi}{4}).     Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11. 1.…

Differentiate w.r.t. x the function in Exercises 1 to 11. 8. (cos{left(acos{x}+bsin{x}right)}), for some constant a and b.     Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in…

Differentiate w.r.t. x the function in Exercises 1 to 11. 7. (left(log{x}right)^{log{x}}), (x>1).     Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11. 1.…

Differentiate w.r.t. x the function in Exercises 1 to 11. 6. ({cot}^{-1}{left[frac{sqrt{1+sin{x}}+sqrt{1-sin{x}}}{sqrt{1+sin{x}}-sqrt{1-sin{x}}}right]}),(0<x<frac{pi}{2}).     Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11. 1. (left(3x^2-9x+5right)^9).…

Differentiate w.r.t. x the function in Exercises 1 to 11. 5. (frac{{cos}^{-1}{frac{x}{2}}}{sqrt{2x+7}}),(-2<x<2).       Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11. 1.…