Find the slope of the tangent line to the curve y = (x)/(1-x) at the point (1/2, 1). Find the equation of that tangent line.

Carsen Patel

Carsen Patel

Open question

2022-08-16

Find the slope of the tangent line to the curve y = x 1 x at the point ( 1 2 , 1 ). Find the equation of that tangent line.

Answer & Explanation

Luna Wells

Luna Wells

Beginner2022-08-17Added 19 answers

y = x 1 x , ( 1 2 , 1 ) d y d x = d d x ( x 1 x ) d y d x = d d x ( x ) ( 1 x ) d d x ( 1 x ) x ( 1 x ) 2               [ since  ( f g ) = f g g f g 2 ] d y d x = 1 ( 1 x ) ( 0 1 ) x ( 1 x ) 2                 [ d d x ( x ) = 1 , d d x ( c o n s t a n t ) = 0 ] d y d x = 1 x + x ( 1 x ) 2 d y d x = 1 ( 1 x ) 2  slope  m = d y d x  at given point  ( 1 2 , 1 ) d y d x | ( 1 2 , 1 ) = 1 ( 1 1 2 ) 2 = 1 ( 1 2 ) 2 = 1 1 4 d y d x = 4 Hence,  Slope  m = 4 L e t ( x 1 , y 1 ) = ( 1 2 , 1 )  The equation of tangent line is,  y y 1 = m ( x x 1 ) y 1 = 4 ( x 1 2 ) y 1 = 4 x 4 2 y 1 = 4 x 2 y = 4 x 2 + 1 y = 4 x 1 Therefore,  Equation of tangent line is,  y = 4 x 1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?