You will need
  • pencil;
  • paper.
Before finding the derivative of a root, note other functions are present in the solved example. If the task includes a lot of radical expressions, use the following rule for finding the derivative of a square root:

(√x)' = 1 / 2√Kh.
For finding the derivative of cube root, apply the formula:

(3√x)' = 1 / 3(3√x)2,

where 3√x denoted the cube root of X.
If in the example are designed for differentiation, is found a variable is in fractional degrees, then slide the designation of the root in a power function with an appropriate indicator. For the square root it will be ½ degree and for cubic root – ⅓:

√x = x ^ ½,
3√x = x ^ ⅓,

where the symbol ^ denotes exponentiation.
To find the derivative of the exponential function in General, and x^½, x^⅓, in particular, use the following rule:

(x ^ n)' = n * x^(n-1).

For the derivative of the square root of this ratio follows:

(x^½)' = ½ x ^ (-½) and
(x^⅓)' = ⅓ x ^ (-⅔).
Differentiating all the roots, carefully take a look at the rest of the example. If the response you got is very cumbersome expression, then surely it can be simplified. Most school samples are composed so that the result is a small number or a compact expression.
Many tasks on finding derivative, roots (square and cube) are found together with other functions. To find the derivative of the root in this case, the following rules apply:
• derivative of a constant (a constant number, C) is zero: C' = 0;
• the constant factor is taken out of the sign of the derivative: (k*f)' = k * (f)' (f is an arbitrary function) ;
• derivative of the sum of several functions is equal to the sum of the derivatives: (f + g)' = (f)' + (g)';
• derivative of product of two functions is equal... no, not the product of the derivatives and the following expression: (fg)' = (f) g + f (g)';
• private derivative also equals no private derivatives is in accordance with the following rules: (f/g)' = ((f) g – f(g)') / g2.