Calculus 220 Part 2 Running Flashcards

Power Rule

$$f^{\prime}(x)=n\cdot x^{n-1}$$

Sum/Difference Rule

\frac{d}{\differentialD x}\left\lbrack f\left(x\right)\pm g\left(x\right)\right\rbrack=f^{\prime}\left(x\right)\pm g^{\prime}\left(x\right)

Product Rule

\frac{d}{\differentialD x}\left\lbrack f\left(x\right)\cdot g\left(x\right)\right\rbrack=f^{\prime}\left(x\right)g\left(x\right)+g^{\prime}\left(x\right)f\left(x\right)

Quotient Rule

\frac{d}{\differentialD x}\left\lbrack\frac{f\left(x\right)}{g\left(x\right)}\right\rbrack=\frac{f^{\prime}\left(x\right)g\left(x\right)-g^{\prime}\left(x\right)f\left(x\right)}{g\left(x\right)^2}

\frac{d}{\differentialD x}\left(\sin x\right)

\frac{d}{\differentialD x}\left(\sin x\right)=\cos x

\frac{d}{\differentialD x}\left(\cos x\right)

\frac{d}{\differentialD x}\left(\cos x\right)=-\sin\left(x\right)

\frac{d}{\differentialD x}\left(\tan x\right)

\frac{d}{\differentialD x}\left(\tan x\right)=\sec^2x

\frac{d}{\differentialD x}\left(\csc x\right)

\frac{d}{\differentialD x}\left(\csc x\right)=-\csc x\cdot\cot x

\frac{d}{\differentialD x}\left(\sec x\right)

\frac{d}{\differentialD x}\left(\sec x\right)=\sec x\cdot\tan x

\frac{d}{\differentialD x}\left(\cot x\right)

\frac{d}{\differentialD x}\left(\cot x\right)=-\csc^2x

Special Cosine Limit

$$\lim_{\theta\to0}\frac{\cos\theta-1}{\theta}=0$$

Special Sine Limit

$$\lim_{\theta\to0}\frac{\sin\theta}{\theta}=1$$

The Chain Rule

$$F^{\prime}\left(x\right)=f^{\prime}\left(g\left(x\right)\right)\cdot g^{\prime}\left(x\right)$$