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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

But try the problem first…

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

Source

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