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In this tutorial, properties of derivatives will be covered, as well as the Power Rule.
Properties of derivatives
The derivative of the sum is the sum of the derivatives:
 \pm g(x))=\frac{df}{dx}\pm\frac{dg}{dx} "\frac{d}{dx}(f(x) \pm g(x))=\frac{df}{dx}\pm\frac{dg}{dx}")
or
\pm g(x))\prime=f\prime(x)\pm g\prime(x) "(f(x)\pm g(x))\prime=f\prime(x)\pm g\prime(x)")
The derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function:
) = k\frac{df}{dx} "\frac{d}{dx}(kf(x)) = k\frac{df}{dx}") where k is some constant
or
)\prime = k f\prime (x) "(k f(x))\prime = k f\prime (x)")
Power Rule
Given a function
=k x^n "f(x)=k x^n")
where k is some constant, and is a coefficient of  , the derivative is
 = k(n)x^{(n-1)} "f\prime(x) = k(n)x^{(n-1)}")
it should also be noted that for
=k "f(x)=k")
where k is some constant, the derivative is
=0 "f\prime(x)=0")
this is true for any constant k
Examples
Find the derivative of the following functions
=5x^2 "1. \,\, f(x)=5x^2")
=5(2)x^{(2-1)}=10x "f\prime(x)=5(2)x^{(2-1)}=10x")
=x+1 "2. \,\, f(x)=x+1")
=(1)x^{(1-1)}+0=(1)x^0+0=1 "f\prime(x)=(1)x^{(1-1)}+0=(1)x^0+0=1")
=x^3+2x^2+3x+1000 "3. \,\, f(x)=x^3+2x^2+3x+1000")
=(3)x^{(3-1)}+2(2)x^{(2-1)}+3(1)x^{(1-1)}+0=3x^2+4x+3 "f\prime(x)=(3)x^{(3-1)}+2(2)x^{(2-1)}+3(1)x^{(1-1)}+0=3x^2+4x+3")
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