To find the derivative of 10x, it is possible to use the power rule for derivatives that is given as d/dx(x^n) = nx^(n-1). To solve this derivation, it is useful to write 10x in the form of a power, such as 10x^1, so that n = 1.
Applying the power rule to 10x^1, the derivative is given as (10)(d/dx)(x^1) = (10)[ 1x^(1 -1)]. This can be written as 10(d/dx)(x^1) = (10)x^0 = 10. The power x^0 is equal to 1, so that the derivative of 10x is equal to 10.
A derivative of a function, such as y = 10x, are useful for finding the slope of the function. In calculus, there are many different rules that apply to finding derivatives.One simple rule is that the derivative of a constant C is zero. Similarly, the derivative of 'x' is 1, or (d/dx)(x) = 1.
Another method to solve for the derivative of 10x is to use this last rule, where the derivative of 'x' is equal to 1. In this case, the derivative is written as (10)(d/dx)(x) = (10)(1) = 10.
Some other derivative rules apply to functions that involve square roots, exponentials, logarithms and trigonometry. Some very common derivatives for ln(x), e^x, and sin(x) are 1/x, e^x and cos(x), respectively.