Question

for what value of x is the derivative of 2x minus x to the power minus 1 is equal to 3​

Answer 1

given, $2x-x^{-1}=3$

or, $2x-\frac{1}{x}=3$

or, $\frac{2x^2-1}{x}=3$

or, $2x^2-1=3x$

or, 2x² - 1 - 3x = 0

or, 2x² - 3x - 1 = 0

or, 2x² - 3x = 1

or, x² - (3/2)x = 1/2

or, x² - 2(3/4)x + (3/4)² = (3/4)² + 1/2

or, (x - 3/4)² = 9/16 + 1/2

or, (x - 3/4)² = 17/16

or, (x - 3/4)² = (√17/4)²

or, x - 3/4 = ± √17/4

or, x = 3/4 + √17/4

hence, value of x = (3 ± √17)/4

Answer 2

Answer:

x = +1 or -1

Explanation:

If we have to take the derivative with respect to "x" then

we are given

Derivative of 2x - x^-1 = 3

⇒       d (2x - x^-1) / dx = 3

Applying derivative with respect to x we get

⇒                       2 + x^-2 = 3

⇒                             x^-2 = 3 - 2

⇒                             x^-2 = 1

⇒                            1 / x² = 1 = 1 / 1

Taking reciprocal on both sides we get

                                   x² = 1

Taking under root on both sides we get

                               √x² = +√1 or -√1

⇒                                 x = +1 or -1  

So the value of x is +1 or -1