What is the solution of the derivative of square root of t divided by the square root of pie?

Answer 1

One expression of the answer is

(square root of pi) / (2*(square root of t)*(pi))

To solve this problem, you will need to apply two differential calculus rules:

1. The constant times a function rule

2. The power rule.

Because it is so hard to write out these rules within the limits of the answers.com display system, you should look up these rules on the internet if you are not familiar with them.

Let SQRT() be the square root function. We are to find the derivative of

SQRT(t)/SQRT(pi)

We can write this as

(1/SQRT(pi)) * SQRT(t), where "*" represents multiplication.

The first factor

(1/SQRT(PI))

is just a constant. However, we often need forms where we remove the SQRT from the denominator. To do so, we multiply the numerator and denominator by SQRT(pi), which gives us

SQRT(pi)/pi

The above expression is the constant we will use when we apply rule 1 above. That constant will remain a factor of the answer, according to the rule.

Next we apply the second rule to

SQRT(t). In order to apply this rule to the expression, we convert the expression to power format. Let ^ represent the exponentiation operator. Then

SQRT(t) = t^(1/2)

Applying the power rule to the second factor of our original expression, we get

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

(1/2) * (1/(t^(1/2) =

(1/2) * (1/(SQRT(t)) =

1 / (2 *SQRT(t))

Combining the factors from the application of both rules we have

( SQRT(pi)/pi ) * (1 / (2 *SQRT(t)) ) =

SQRT(pi) / (2 * SQRT(t) * pi) = (the answer given above)

SQRT(pi) / (2 * pi * SQRT(t)) = an equivalent answer

(SQRT(pi) * SQRT(t)) / (2 * pi * t) = another equivalent answer

(SQRT(pi * t)) / (2 * pi * t) = another equivalent answer.

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Answer #2:

Wow! If that kind of problem had required that kind of work,

I'm afraid I would have dropped Calculus, and missed out on

the fun of Math and Engineering completely.

How about 1/sqrt(pi * t) ?