derivative???

Question

How do you solve for the derivative ?? could you please give an example for better understanding...

thanks ^_^

Answer 1

The simplest derivatives are where there is some power to a variable.

Take the power of the variable, stick it in front of the variable as a multiplier, then subtract 1 from the power. This can be done for each term of a function.

Nomenclature: if a is a function a' is its derivative.

Examples:
a(b) = 19*b (power of b is 1, stick it in front as a multiplier, this time no change)
a'(b) = 19 (subtract 1 from the power which is b^1, b^0 =1 so b disappears)

or

a(b) = -2*b^4 (take the power, and stick it in front as a multiplier)
a'(b) = 4* -2*b^3 (subtract 1 from the variable's power, 4, leaving b^3)
a'(b) = -8*b^3

a(b) = 12 (in this case, b is actually b^0 = 1. Take the power, stick in front as a multiplier, and ....)
a'(b) = 0 * 12 (even if we had to consider adding b^-1, who cares? 0 times anything is still 0)
a'(b) = 0

Now try it where they are chained together:
a(b) = 19*b - 2*b^4 +12

This is where the old "The sum of the derivative is the derivative of the sum" comes into play, because you can take the derivative of each term of the function individually, just liek above, so:
a'(b) = 19 - 8*b^3 + 0

Once you have your final derivative, the value of the variable (in my repetitive examples, b) where the derivative = 0 is a local minimum or maximum for the function.

I hope that helps somewhat. This is a very simplified explanation.

Answer 2

Take the value of the exponent of the variable and multiply it by the original function's coefficient. Then, bring the exponent back to the variable and decrease its value by 1.
2x^2 becomes 4x^1 or 4x

If it's a variable with an exponent of 1, just take away the variable.
So the derivative of 7x=7

For a lone constant, the derivative is 0.
Derivative of 8=0. The derivative of 2,865 is also 0.

Answer 3

The universal method to find a derivative is

f'(x) = lim(as h -> 0) of (f(x + h) - f(x)) / h.

However, the derivatives of many types of common functions are well-known and are tabulated, as are various properties of the derivative. One example is that the derivative of x^n will be equal to n*x^(n - 1). Another is that (f + g)' = f' + g', where the tick mark ' is a shorthand for the derivative.

Answer 4

Well, you question is the equivalent of asking "How do you solve for the sum". Well you add the numbers together. To solve for the derivative, you differentiate. Try googling "how to solve derivates" if you do not know how.

Answer 5

limit of different quotient as h approaches 0