Review the differentiation rules for all the common function types.

Polynomials

start fraction, d, divided by, d, x, end fraction, left parenthesis, a, x, start superscript, n, end superscript, right parenthesis, equals, a, dot, n, x, start superscript, n, minus, 1, end superscript
Want to learn more about differentiating polynomials? Check out this video.

Radicals

Want to learn more about differentiating radicals? Check out this video.

Trigonometric functions

start fraction, d, divided by, d, x, end fraction, sine, left parenthesis, x, right parenthesis, equals, cosine, left parenthesis, x, right parenthesis
start fraction, d, divided by, d, x, end fraction, cosine, left parenthesis, x, right parenthesis, equals, minus, sine, left parenthesis, x, right parenthesis
ddxtan(x)=sec2(x)=1cos2(x)\dfrac{d}{dx}\tan(x)=\sec^2(x)=\dfrac{1}{\cos^2(x)}
ddxcot(x)=csc2(x)=1sin2(x)\dfrac{d}{dx}\cot(x)=-\csc^2(x)=-\dfrac{1}{\sin^2(x)}
ddxsec(x)=sec(x)tan(x)=sin(x)cos2(x)\dfrac{d}{dx}\sec(x)=\sec(x)\tan(x)=\dfrac{\sin(x)}{\cos^2(x)}
ddxcsc(x)=csc(x)cot(x)=cos(x)sin2(x)\dfrac{d}{dx}\csc(x)=-\csc(x)\cot(x)=-\dfrac{\cos(x)}{\sin^2(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

start fraction, d, divided by, d, x, end fraction, left parenthesis, e, start superscript, x, end superscript, right parenthesis, equals, e, start superscript, x, end superscript
start fraction, d, divided by, d, x, end fraction, left parenthesis, a, start superscript, x, end superscript, right parenthesis, equals, natural log, left parenthesis, a, right parenthesis, dot, a, start superscript, x, end superscript
Want to learn more about differentiating exponential functions? Check out this video.

Logarithmic functions

start fraction, d, divided by, d, x, end fraction, natural log, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, x, end fraction
start fraction, d, divided by, d, x, end fraction, log, start subscript, b, end subscript, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, natural log, left parenthesis, b, right parenthesis, x, end fraction
Want to learn more about differentiating logarithmic functions? Check out this video.

Inverse trigonometric functions

ddxarcsin(x)=11x2\dfrac{d}{dx}\arcsin(x)=\dfrac{1}{\sqrt{1-x^2}}
ddxarccos(x)=11x2\dfrac{d}{dx}\arccos(x)=-\dfrac{1}{\sqrt{1-x^2}}
ddxarctan(x)=11+x2\dfrac{d}{dx}\arctan(x)=\dfrac{1}{1+x^2}
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.