## Onmatu- Calculus Article

#### Article Author

#### Alexandra Lecic

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# Derivation

Because the first derivative represents a slope of the tangent line of the given function and f(x)=x is a straight line.

What happens with a function f(x)=x^2? Its first derivative is f'(x)=2x. You can try to draw a tangent line at some point, let's say x = 1 and calculate its slope. You should get 2.

For function f(x) = x^3, we have f'(x) = 3x^2.

And, in general we have that the first derivative of a function f(x) = x^n is f'(x) = nx^{n-1}, n is a real number.

For the square root (we denote it by sqrt) we have a rule that is a consequence of the rule above:

(sqrt(x))' = 1/(2sqrt(x)).

Tha first derivative of a function f(x) = lnx is

f'(x) = 1/x.

Let's take a look at derivatives of trig. functions.

(sinx)' = cosx

(cosx)' = -sinx

(tanx)' = 1/cos^2(x)

(cotx)' = -1/sin^2(x)

We continue in the next lesson.