Differentiation

Blue = on formula sheet

Differentiating Trig functions (important)

y = sin f(x) ---> dy/dx = f '(x) cos f(x)

y = cos f(x) ---> dy/dx = - f '(x) sin f(x)

y = tan f(x) ---> dy/dx = f '(x) secē f(x)

y = cosec f(x) ---> dy/dx = - f '(x) cosec f(x) cot f(x)

y = sec f(x) ---> dy/dx = f '(x) sec f(x) tan f(x)

y = cot f(x) ---> dy/dx =- f '(x) cosecē f(x)


Other differentials (important)

y = e^f(x) ---> dy/dx = f '(x) e^f(x)

y = ln f(x) ---> dy/dx = f '(x) / f(x)


Chain Rule

Quicker method

n x f '(x) ( f(x) )^n-1


Product Rule


Quotient Rule


Finding a tangent to a curve

Find dy/dx then sub into y - y1 = m (x - x1)


Finding minimum and maximum