Definition of the Derivative help

Derivative means the answer you get after you differentiated the function.

So if f(x)=-5

f'(x)=0, the derivative of a constant is 0

if f(x)=3x-7

f'(x)=3, because the derivative of a constant is 0 and the derivative of 3x =3 so 3-0=3

So how do you get differentiate 3x? Well you different by rule: if f(x)=ax^n then f'(x)=nax^(n-1)

So, 3x=3x^1 according to the rule, the derivative of 3x=1*3x^(1-1)

Therefore, it is 3x^0 and it is equals to 3.

If f(x)=2-3x^2

=-3x^2+2

=-6x Why? Same logic as explained above.

If f(x) 5x/3+x Now, here you have to use the quotien rule: if f(x)=u/v then f'(x)= ((v*u') - (u*v'))/(v^2)

Let 5x=u and 3+x=v

u'=5 and v'=1

So f'(x)=((5(3+x)) - (5x))/(3+x)^2

=15/(3+x)^2 and simply if required.

And dont lie about your age.

A derivative is the line tangent to a point on a curve.

try Khanacademy.org for a lesson on how to find derivatives.

Lets say you have a funtion f(x) that is continuous on some interval (a,b) in x. This about the graph of this function - it isome sort of curve in the x,y plane. At any point on this curve (in the interval (a,b)) you can estimate the slope of the function (the rate of change of f(x) with respect to x) by drawing a straight line tha tis tangent to th epoint on the curve. The slope of that line gives you the instantaneous rate of change - that is, the rate of change of the function f(x) at the point where you've constructed this tangent line.

So how do we compute this mathematically - it is impractical to draw tangent lines over the graphs on functions - and it is of limited utility. This is where teh operation of differntiation comes in. The derivative of a function is the instantenous rate of change of the function and is defined by the limit process: