Higher - Order
derivatives
BASIC CALCULUS
Objectives
1.
TO KNOW THE HIGHER - ORDER
DERIVATIVE
2.
TO DETERMINE THE HIGHER ORDER
DERIVATIVE OF A FUNCTION
Higher - Order
Derivatives
Higher-order derivatives are simply the derivative of
a derivative. You would use the same derivative rules
that you learned for finding the first derivative of a
function.
Higher - Order
Derivatives
Is when we take the derivative of the function ƒ(x), the
derivative ƒ'(x) is called the first derivative. Taking the
derivative of the first derivative would, in turn, give us the
second derivative, and so on
Higher - Order
Derivatives
EXAMPLES
Find the fourth - derivative of:
ƒ(x) = 3x⁵ - 2x⁴ + 5x² - 7x + 1
Find the first - derivative of:
ƒ(x) = 2x² + 3x² - 12x + 5
Find the second - derivative of:
ƒ(x) = 5x³ + sinx
EXAMPLES
Find the third - derivative of:
y = sin²x
Find the first - derivative of:
g(x) = sine4x
EXAMPLES
MALUNAO
MANALO
TY
GONZALES
LENDIO
MALUNAO
MANALO
GONZALES
LENDIO