Category: Continuity and Differentiability

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

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

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.

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

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.

Differentiate w.r.t. x the function in Exercises 1 to 11. 7. (left(log{x}right)^{log{x}}), (x>1).     Continuity and Differentiability

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

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

Differentiate w.r.t. x the function in Exercises 1 to 11. 4. ({sin}^{-1}{left(xsqrt xright)}),(0le xle1).     Continuity and

Differentiate w.r.t. x the function in Exercises 1 to 11. 3. (left(5xright)^{3cos{2}x}).   Continuity and Differentiability Miscellaneous Exercise