- #1
jhodzzz
- 15
- 0
what is the first derivative of f(x)=(1-x)^{2}(1+x)^{3}?
The derivative of f(x)=(1-x)2(1+x)3 is -10x^{4}+16x^{3} -10x^{2}+4x+5.
The derivative of a function is found by using the power rule, product rule, and chain rule in calculus. In this case, we would first use the power rule to find the derivative of each term, then use the product rule to combine them.
The derivative of a function represents the rate of change of the function at a specific point. In this case, it tells us how fast the function is changing at any given value of x.
The derivative can be used in various fields such as physics, economics, and engineering to analyze and predict changes in a system. For example, in economics, the derivative can be used to determine the marginal cost and revenue of a company.
The derivative of this function follows the general rules of differentiation, but it is always important to check for any potential special cases or exceptions. In this case, we would need to ensure that the derivative exists at all points of the function and that there are no undefined or discontinuous points.