19. Using the fact that (sin{(A+B)}=sin{A}cos{B}+cos{A}sin{B}) and the differentiation, obtain the sum formula for cosines. 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.…
18. If (fleft(xright)=left|xright|^3), show that f”(x) exists for all real x and find it. 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).…
17. If (x=aleft(cos{t}+tsin{t}right) ) and (y=aleft(sin{t}-tcos{t}right)), find (frac{d^2y}{dx^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…
16. If (cos{y}=xcos{left(a+yright)} ) with (cos{a}neqpm1), prove that (frac{dy}{dx}=frac{{cos}^2{left(a+yright)}}{sin{a}}). 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.…
15. If (left(x-aright)^2+left(y-bright)^2=c^2), for some c>0, prove that (frac{left[1+left(frac{dy}{dx}right)^2right]^frac{3}{2}}{frac{d^2y}{dx^2}}) is a constant independent of 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 Exercises 1 to…
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…
