Basic Derivative
f(x^n)= nX^(n-1)
A derivative is a mathematical concept that measures the rate at which a function changes. It is denoted by the symbol dy/dx and is pronounced as dee y by dee x. A derivative can be computed for any type of function and is used extensively in calculus and related fields.
To find the derivative of a function, you need to follow the steps given below:
1. Write the function using proper notation.
2. Identify the variable that you want to differentiate with respect to. This is usually denoted as x in the equation.
3. Determine the power or exponent of this variable.
4. Multiply the coefficient (if any) by the exponent and subtract 1 from the exponent.
5. Rewrite the coefficient and exponent in the answer to the first derivative.
6. Simplify the result by removing any unnecessary terms.
For example, let’s consider the function f(x) = 3x^2 + 2x – 5.
1. The function is given as f(x) = 3x^2 + 2x – 5.
2. We want to differentiate with respect to x.
3. The variable x is raised to the power of 2.
4. Applying the power rule, we multiply the coefficient 3 by the exponent 2 to get 6, and subtract 1 from the exponent to get 1. We also multiply the coefficient 2 by the exponent 1 to get 2.
5. Therefore, the first derivative of f(x) is:
f'(x) = 6x + 2.
6. The result can be simplified by removing any unnecessary terms, so the final answer would be:
f'(x) = 6x + 2.
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