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) ?
The square root of x = x to the power of a half
The derivative of sqrt(2) is zero.
Use the formula for the derivative of a power. The square root of (x-5) is the same as (x-5)1/2.
The square root of six divided by the square root of two equals the square root of three.
The derivative of cos x is -sin x, the derivative of square root of x is 1/(2 root(x)). Applying the chain rule, the derivative of cos root(x) is -sin x times 1/(2 root(x)), or - sin x / (2 root x).
The square root of x = x to the power of a half
the derivative is 0. the derivative of a constant is always 0.
The derivative of sqrt(2) is zero.
The solution to -3 times the square root of 184 divided by 4 is approximately equal to -12.94.
Use the formula for the derivative of a power. The square root of (x-5) is the same as (x-5)1/2.
The square root of six divided by the square root of two equals the square root of three.
The derivative of cos x is -sin x, the derivative of square root of x is 1/(2 root(x)). Applying the chain rule, the derivative of cos root(x) is -sin x times 1/(2 root(x)), or - sin x / (2 root x).
0.625
It is negative one divided by 4 multiplied by x to the power of 1.5 -1/(4(x^1.5))
3/(4*square root(x)) ....Mukesh
0.6667
The square root of pi divided by seven is 0.253207693