Calc BC Unit 2 formula review

Derivative of sinx

cosx

Derivative of tanx

sec²x

Derivative of secx

secx tanx

Derivative of cosx

-sinx

Derivative of cotx

-csc²x

Derivative of cscx

-cscx cotx

derivative of arcsin

$$\frac{1}{\sqrt{1-x^2}}$$

derivative of arccos

$$-\frac{1}{\sqrt{1-x^2}}$$

derivative of arctan

$$\frac{1}{1+x^2}$$

$$\int^{}\sin u\,dx$$

$$-\cos u+c$$

$$\int^{}\cos u\,dx$$

sinu + c

$$\int^{}\tan u\,dx$$

$$-\ln\left\vert\cos u\right\vert+c$$

$$\int^{}\cot u\,dx$$

$$\ln\left\vert\sin u\right\vert+c$$

$$\int^{}\sec u\,dx$$

$$\ln\left\vert\sec u+\tan u\right\vert+c$$

$$\int^{}\csc u\,dx$$

$$-\ln\left\vert\csc u+\cot u\right\vert+c$$

$$\int^{}\sec^2u\,dx$$

$$\tan u+c$$

$$\int^{}\csc^2u\,dx$$

-cotu+c

$$\int^{}\sec u\tan u\,dx$$

secu+c

$$\int^{}\csc u\cot u\,dx$$

-cscu+c

$$\frac{du}{\sqrt{a^2-u^2}}$$

$$\arcsin\frac{u}{a}$$

$$\frac{du}{a^2+u^2}$$

$$\frac{1}{a}\arcsin\frac{u}{a}$$

$$\frac{du}{\sqrt{a^2-u^2}}$$

$$\frac{1}{a}\frac{\operatorname{arcsec}u}{a}$$

sin²x+cos²x =

1

sin²x =

$$\frac{1-\cos2x}{2}$$

cos²x =

$$\frac{1+\cos2x}{2}$$

if sine is odd and positive

keep one sine and convert rest to cosines

if cosine is odd and positive

keep one cosine and convert rest to sines

sinmxsinnx

½ (cos[(m-n)x]-cos[(m+n)x])

sinmxcosnx

½ (sin[(m-n)x]+sin[(m+n)x])

cosmxcosnx

½ (cos[(m-n)x]+cos[(m+n)x])

$$\sqrt{a^2+x^2}$$

$$a\sin\theta$$

$$\sqrt{a^2+x^2}$$

$$a\tan\theta$$

$$\sqrt{x^2-a^2}$$

$$a\sec\theta$$

1-sin²$\theta$

cos^$\theta$

1+tan²$\theta$ 

sec²$\theta$ 

sec²$\theta$ -1

tan²$\theta$

\int_1^{\infty}\!\frac{dx}{x^{p}}\,p>1

$$\frac{1}{p-1}$$

\int_1^{\infty}\!\frac{dx}{x^{p}}\,p<1

diverges