Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Derivative.

Derivative Problem (B.Stat Objective Question )


If y=\(3^\frac{sinax}{cosbx}\), then \(\frac{dy}{dx}\) is

  • \(3^\frac{sinax}{cosbx}\frac{acosaxcosbx-bsinaxsinbx}{cos^{2}bx}log3\)
  • \(3^\frac{sinax}{cosbx}\frac{acosaxcosbx+bsinaxsinbx}{cos^{2}bx}log3\)
  • \(3^\frac{sinax}{cosbx}log3\)
  • \(3^\frac{sinax}{cosbx}\)

Key Concepts


Equation

Derivative

Algebra

Check the Answer


But try the problem first…

Answer:\(3^\frac{sinax}{cosbx}\frac{acosaxcosbx+bsinaxsinbx}{cos^{2}bx}log3\)

Source
Suggested Reading

B.Stat Objective Problem 764

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

\(y=3^\frac{sinax}{cosbx}\)

or, \(\frac{dy}{dx}\)=\(3^{\frac{sinax}{cosbx}}log_{e}{3}\frac{d}{dx}\frac{sinax}{cosbx}\)

Second Hint

or, \(\frac{dy}{dx}\)=\(3^{\frac{sinax}{cosbx}}log_{e}{3}{\frac{cosbxcosaxa-sinax(-sinbx)b}{cos^{2}bx}}\)

Final Step

or, \(3^\frac{sinax}{cosbx}\frac{acosaxcosbx+bsinaxsinbx}{cos^{2}bx}log3\)

Subscribe to Cheenta at Youtube