Question

if x=√t+1/√t,then dx/dt is equal to? Explain in steps? ​

Answer 1

Answer:

HOPE THE ATTACHMENT HELPS YOU

Answer 2

Answer:

Hence the required answer is

(d) 1/(2√t ) - 1/( 2t√t )

Step-by-step explanation:

We will use the formula

d/dx ( x^m) = m x^( m - 1)

Now it is given that

x = √t + (1 /√t ) = t^(1/2) + t^(-1/2)

Now Differentiating both sides with respect to t we get

dx/dt

= d/dt [ t^(1/2) + t^(-1/2)]

= d/dt [ t^(1/2) ] + d/dt [ t^(-1/2)]

= (1/2) t^(1/2 - 1 ) - (1/2) t^(-1/2-1 ) ( using the formula)

= (1/2) t^( - 1/2 ) - (1/2) t^( - 3/2 )

= 1/(2√t ) - 1/( 2t√t )

Hence the required answer is (d) 1/(2√t ) - 1/( 2t√t )