JEE Main201815 Apr 2018Evening ShiftMathematicsDifferentiationActual

If f(x)= ⁻¹ ( 2 3^x 1+9^x ) , then f^ (- 1 2 ) equals.

Options

A3 _e 3
B- 3 _e 3
C- 3 _e 3
D3 _e 3

Correct answer

A. 3 _e 3

Step-by-step solution

Since f(x)= ( 2 3^x 1+9^x ) Suppose 3^x= t aligned & f(x)= ⁻¹ ( 2 t 1+ ^2 t ) &= ⁻¹( 2 t)=2 t=2 ⁻¹(3 x) & So, f^ (x)= 2 1+ (3^x )^2 3^x _e 3 & f^ (- 1 2 )= 2 1+ (3^ - 1 2 )^2 3^ - 1 2 _e 3 &= 1 2 3 _e 3= 3 _e 3 aligned

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