derivative rules (save me)

(d/dx) x^n

nx^(n-1)

(d/dx) y

(dy/du)(du/dx)

(d/dx) uv

(v * du/dx) + (u * dv/dx)

(d/dx) u/v

(v * du/dx - u * dv/dx) / v²

(d/dx) log_a(x)

1 / (x * ln(a))

(d/dx) a^x

a^x * ln(a)

(d/dx) e^x

e^x

(d/dx) ln(x)

1/x

(d/dx) sin(x)

cos(x)

(d/dx) cos(x)

-sin(x)

(d/dx) tan(x)

sec²(x)

(d/dx) csc(x)

-csc(x) * cot(x)

(d/dx) sec(x)

sec(x)*tan(x)

(d/dx) cot(x)

-csc(x²)