How do you find the derivative?

Answer by  Tear (27)

This is a complex question that can have many answers depending on the numbers and formulas used. The basic rule is f(x) = x^r, then the derivative, f'(x) = r*x^(r-1). So if you had x^2 then your answer would be 2x. There are many other rules out there, depending on what you are doing, however.

Answer by  CR125 (396)

There are many ways: power rule, chain rule, product rule, and quotient rule. If differentiating in terms of x, you need to use implicit differentiation. For natural log functions, natural exponential functions, and logarithmic differentiation there are specific ways for this as well.

Answer by  john11 (617)

It depends on what function you want the derivative of. For polynomials of the form x^n, the derivative is n*x^(n-1). For exponential functions of the form e^(n*x), the derivative is n*e^(n*x). For the trigonometric functions the derivatives are: d/dx[sin(x)] => (cos(x), d/dx[cos(x)] => -sin(x), d/dx[tan(x)] = d/dx[sin(x)/cos(x)] = d/dx[sin(x)*(cos(x))^-1] => cos(x)/cos(x) + sin^2(x)*(cos(x))^-2 = 1 + tan^2(x) = sec^2(x).