Home
Class 12
MATHS
Let z=(cosx)^5 and y="sin"xdot Then the ...

Let `z=(cosx)^5 and y="sin"xdot` Then the value of `(d^2z)/(dy^2)a tx=(2pi)/9` is____________.

Text Solution

AI Generated Solution

To solve the problem step by step, we start with the given functions and apply differentiation accordingly. ### Step 1: Define the functions Let \( z = (\cos x)^5 \) and \( y = \sin x \). ### Step 2: Differentiate \( z \) with respect to \( x \) Using the chain rule and the power rule: \[ ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Archives|14 Videos
  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Matrix Match Type|6 Videos
  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos
  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Let z=(cosx)^5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=(2pi)/9 is____________.

Let z=(cosx)^5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=(2pi)/9 is____________.

Plot y=sinxa n dy=sin2xdot

Plot y=sinxa n dy=sin2xdot

Plot y=sinxa n dy=sin2xdot

If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value of (a^2)/(b^2) is_______

If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value of (a^2)/(b^2) is_______

If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value of (a^2)/(b^2) is_______

If cos(2sin^(-1)x)=1/9, then find the values of xdot

If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2), then A=x^(2)+y^(2)+z^(2) . (sin^(-1)x)^(2)+(sin^(-1)y)^(2)+(sin^(-1)z)^(2)=(3pi^(2))/(4) , then B=|(x+y+z)_("min")| . Then the value of (A+B) is _____________ .

CENGAGE ENGLISH-DIFFERENTIATION-Numerical Value Type
  1. A nonzero polynomial with real coefficients has the property that f(x)...

    Text Solution

    |

  2. A function is reprersented parametrically by the equations x=(1+t)/(t^...

    Text Solution

    |

  3. Let z=(cosx)^5 and y="sin"xdot Then the value of (d^2z)/(dy^2)a tx=(2p...

    Text Solution

    |

  4. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

    Text Solution

    |

  5. "Let "f(x)=x + (1)/(2x + (1)/(2x + (1)/(2x + .....oo))). Then the v...

    Text Solution

    |

  6. Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are...

    Text Solution

    |

  7. "If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)...

    Text Solution

    |

  8. Let f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))), where -pi/4...

    Text Solution

    |

  9. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

    Text Solution

    |

  10. Let f: R->R be a differentiable function with f(0)=1 and satisfy...

    Text Solution

    |

  11. f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(p...

    Text Solution

    |

  12. If y=f(x) is an odd differentiable function defined on (-oo,oo) such T...

    Text Solution

    |

  13. If x^(3)+3x^(2)-9x+lamda is of the form (x-alpha)^(2)(x-beta) then lam...

    Text Solution

    |

  14. If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(...

    Text Solution

    |

  15. Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value ...

    Text Solution

    |

  16. y=f(x) , where f satisfies the relation f(x+y)=2f(x)+x y(y)+ysqrt(f(x)...

    Text Solution

    |

  17. If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime...

    Text Solution

    |

  18. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

    Text Solution

    |

  19. lim(hrarr0) ((e+h)^(In(e+h))-e)/(h) is-

    Text Solution

    |

  20. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

    Text Solution

    |