gugugh

d/dx [sin x] = cos x

d/dx [cos x] = -sin x

d/dx [tan x] = sec^2 x

d/dx [csc x] = -csc x cot x

d/dx [sec x] = sec x tan x

d/dx [cot x] = -csc^2 x

d/dx1 [x^n] = nx^(n-1)

d/dx [c] = 0

d/dx [c f(x)] = c f'(x)

d/dx [f(x) ± g(x)] = f'(x) ± g'(x)

d/dx [sin^(-1) x] = 1/√(1-x^2)

d/dx [cos^(-1) x] = -1/√(1-x^2)

d/dx [tan^(-1) x] = 1/(1+x^2)

d/dx [cot^(-1) x] = -1/(1+x^2)

d/dx [sec^(-1) x] = 1/(|x|√(x^2-1))

d/dx [csc^(-1) x] = -1/(|x|√(x^2-1))

d/dx [e^x] = e^x

d/dx [a^x] = a^x ln a

d/dx [ln x] = 1/x

d/dx [log_a x] = 1/(x ln a)

You got it! Here are all the integrals and their solutions from the image in plain text:

int(1/√(1-x^2) dx) = sin^(-1) x + C

int(1/(1+x^2) dx) = tan^(-1) x + C

int(1/(|x|√(x^2-1)) dx) = sec^(-1) x + C

int(sin^n (x) dx) = -1/n sin^(n-1)(x) cos(x) + (n-1)/n int(sin^(n-2)(x) dx)

int(cos^n (x) dx) = 1/n cos^(n-1)(x) sin(x) + (n-1)/n int(cos^(n-2)(x) dx)

int(tan^n (x) dx) = 1/(n-1) tan^(n-1)(x) - int(tan^(n-2)(x) dx)

int(sec^n (x) dx) = 1/(n-1) sec^(n-2)(x) tan(x) + (n-2)/(n-1) int(sec^(n-2)(x) dx)

int(csc^n (x) dx) = -1/(n-1) csc^(n-2)(x) cot(x) + (n-2)/(n-1) int(csc^(n-2)(x) dx)