Derivative rules

(d/dx)x^r

rx^(r-1)

Let c be a constant.

Then d/dxc=0

(d/dx) (f(x)+g(x))

(d/dx)f(x)+(d/dx)g(x)

(d/dx)(c f (x))

c f’(x) where c is a constant 

(d/dx)(f(x)g(x))

f’(x)g(x)+f(x)g’(x) (product rule)

(d/dx)(f(x)/g(x)

(g(x)f’(x)-f(x)g’(x)/[g(x)]²

(d/dx)a^x

a^xln(a)

(d/dx)e^x

e^x

(d/dx)ln(x)

1/x

(d/dx)loga(x)

1/xln(a)

(d/dx)sinx

cos(x)

(d/dx)cosx

-sin(x)

(d/dx)tanx

sec²x

(d/dx)csc(x)

-cscxcotx

(d/dx)secx

secxtanx

(d/dx)cotx

-csc²x

(d/dx)[f(x)^r

r[f(x)]^r-1 *f(x)

(d/dx)a^f(x)

f’(x)* a^f(x)*ln(a)

(d/dx)e^f(x)

f’(x)e^f(x)

(d/dx)ln(f(x))

f’(x)/f(x)

(d/dx)loga(f(x))

f’(x)/f(x)ln(a)

(d/dx)sin(f(x))

f’(x)cos(f(x))

(d/dx)cos(f(x))

-f’(x)sin(f(x))

(d/dx)tan(f(x))

f’(x)sec²(f(x))

(d/dx)csc(f(x))

-f’(x)csc(f(x))cot(f(x))

(d/dx)sec(f(x))

f’(x)sec(f(x))tan(f(x))

(d/dx)cot(f(x))

-f’(x)csc²(f(x))