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Common derivatives review

Review the differentiation rules for all the common function types.

Polynomials

ddx(axn)=anxn1
Want to learn more about differentiating polynomials? Check out this video.

Radicals

ddxAxnm=ddx(xnm)=nmxnm1
Want to learn more about differentiating radicals? Check out this video.

Trigonometric functions

ddxsin(x)=cos(x)
ddxcos(x)=sin(x)
ddxtan(x)=sec2(x)=1cos2(x)
ddxcot(x)=csc2(x)=1sin2(x)
ddxsec(x)=sec(x)tan(x)=sin(x)cos2(x)
ddxcsc(x)=csc(x)cot(x)=cos(x)sin2(x)
Want to learn more about differentiating trigonometric functions? Check out this video about sine and cosine, this video about tangent and cotangent, and this video about secant and cosecant.

Exponential functions

ddx(ex)=ex
ddx(ax)=ln(a)ax
Want to learn more about differentiating exponential functions? Check out this video.

Logarithmic functions

ddxln(x)=1x
ddxlogb(x)=1ln(b)x
Want to learn more about differentiating logarithmic functions? Check out this video.

Inverse trigonometric functions

ddxarcsin(x)=11x2
ddxarccos(x)=11x2
ddxarctan(x)=11+x2
Want to learn more about differentiating inverse trigonometric functions? Check out this video about the inverse sine, this video about the inverse cosine, and this video about the inverse tangent.

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