Question

differntiate with respect to x: 1/√x+a-√x​

Answer 1

Step-by-step explanation:

Here we are using the formula

differentiation of x^n is nx^(n-1)

differentiation of x^(1/2) is (1/2)x^(1/2-1)

(1/2)x^(-1/2)

(1/2)* 1/x^(1/2)

1/(2*x^(1/2))

$1 \div 2 \sqrt{x}$

differentiation of

$1 \div \sqrt{x}$

or

x^(-1/2) is (-1/2)x^(-1/2-1)

(-1/2) * x^(-3/2)

(-1/2) * 1/(x^(3/2))

-1/(2*x^(3/2))

differentiation of constant is 0. so for a it is 0

The whole answer is

1/(2x^(1/2))-1/(2x^(3/2))

In this two terms common number is 1/2

so we take 1/2 as common number

(1/2)(1/x^(1/2)-1/x^(3/2))

Here we take LCM

(1/2) ( (x ^ (3/2)-x ^ (1/2)) / (x ^ (1/2+3/2) )

(1/2) ( (x ^ (3/2)-x ^ (1/2)) / (x ^ (4/2) )

(1/2) ( (x ^ (3/2)-x ^ (1/2)) / (x ^ 2) )

(1/2x^2)(x ^ (3/2)-x ^ (1/2))

Answer 2

Step-by-step explanation:

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