worked example: Find the derivative of f(x)=4x2
f′(x)=4⋅dxd[x2]
f′(x)=4⋅2x
worked example: Find the derivative of f(x)=2x7
f′(x)=(7)(2)x7−1=14x6
worked example: Find the derivative of f(x)=4x2+5
f′(x)=dxd[4x2]+dxd[5]
f′(x)=8x+0
worked example: Find the derivative of f(x)=4x2+5x
f′(x)=dxd[4x2]+(5)dxd[x]
f′(x)=8x+(5)(1)
worked example: Find the derivative of f(x)=4x2+5x+6
f′(x)=dxd[4x2]+(5)dxd[x]+dxd[6]
f′(x)=8x+5+0
worked example: Find f′(1) for f(x)=5x3+2x+5
f′(x)=15x2+2
f′(1)=17
worked example: Differentiate f(x)=x−21
f′(x)=−21⋅x−23
f′(x)=−21⋅(x)31
worked example: Differentiate f(x)=2x1+x3
f′(x)=(21)dxd[x]+dxd[x2]
f′(x)=21+2x
worked example: Differentiate f(x)=x1+x1
f(x)=x−1+x−21
f′(x)=(−1)x−2+(−21)x−23
worked example: Differentiate f(x)=2x2−x1
f(x)=2x2−x−1
f′(x)=4x+x21
worked example: Differentiate f(x)=2x2−7x+3x−3 by factorizing first
f(x)=2x2−6x−x+3x−3
f(x)=2x(x−3)+(−1)(x−3)x−3
f(x)=(2x−1)(x−3)x−3
f(x)=2x−11
f′(x)=(−1)(2x−1)−2
f′(x)=(2x−1)2−1
worked example: Differentiate f(x)=3x2−5x−2x−2 by factorizing first
f(x)=3x2−6x+x−2x−2
f(x)=3x(x−2)+1(x−2)x−2
f(x)=(3x+1)(x−2)x−2
f(x)=3x+11
f′(x)=(−1)(3x+1)−2
f′(x)=(3x+1)2−1
worked example: Differentiate f(x)=e5x+e7−e−x
f′(x)=5e5x+0+e−x
worked example: Differentiate f(x)=−2x1
f(x)=−21x−21
f′(x)=41x−23
worked example: Differentiate f(x)=exe2x−ex+1
f(x)=exe2x−1+ex1
f(x)=ex−1+ex1
f(x)=ex−1+e−x
f′(x)=ex−e−x
worked example: Differentiate f(x)=x31−x22
f(x)=x−3−2⋅x−2
f′(x)=−3x−4+4x−3