## Journal Journal: yo

If f'(x) > 0 on an interval, then f is increasing on that interval

If f(x) 0 on an interval, then f is decreasing on that interval

d/dx (constant number) = 0

d/dx (x) = 1

d/dx (x^n) = nx^(n-1)

If C is constant and f is differentiable, d/dx (cf(x)) = c*d/dx(f(x))

if f and g are differentiable, d/dx (f(x) + (g(x)) = d/dx (f(x)) + d/dx(g(x))

if f and g are differentiable, d/dx (f(x) - (g(x)) = d/dx (f(x)) - d/dx(g(x))

d/dx(e^x) = e^x

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

d/dx(f(x)/g(x)) = g(x)d/dx(f(x)) - f(x)d/dx(g(x))/(g(x)^2

d/dx(a^x) = a^x(ln(a))

if f and g are both differentiable and F(x) = f(g(x)), then F' = f'(g(x))*g(x)

dy/dx= dy/dt/dx/dt

two curves are called orthogonal if at each point of intersection, d/dx(f) is the inverse reciprical of d/dx(g)

d/dx(log(x)/log(a) = 1/x*ln(a)

d/dx(ln(x)) = 1/x

TANGENT LINE: y =f(a) + f'(a)(x-a)

AVERAGE RATE OF CHANGE (over a,b) = f(b)-f(a) / b -a

INSTANT RATE OF CHANGE = y2-y1 / x2-x1