matematika terapan week 12
TRANSCRIPT
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
TIF 21101APPLIED MATH 1
(MATEMATIKA TERAPAN 1)
Week 12Derivative
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
The derivative of a function gives the gradient function.
i.e. the instantaneous rate of change of function f(x).
Differentiation is the process of determining the derivative from a given function.
Thus, this implies that…
the derivative f’(x) is found by the differentiation of function f’(x)
Derivative
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Derivative
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
DerivativeBefore we learn the derivative, there are some terms you need understand. The sysmbol of d/dx (something) means “the derivative of (something) with respect to x.”
This is how we say this aloud. The symbol d/dx is an operator; it is telling you to do something, just in the same way the symbol “+” tells you to do something in the expression 5 + 3. After you do what it tells you, it disappears; exactly the same way 5 + 3 = 8, not 8+. This operator takes a single input (called an argument) and gives you a single function as an output.
The symbol f ’(x) means the same thing as above; this is the derivative of the function f with respect to x.
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Derivative
(something) dx means “the antiderivative of (something) with respect to x.”
This is how we say this aloud. The symbols dx are again an operator; they are telling you to do something. Again, they go away after you do what it tells you to do. This operator takes a single input and gives you a family of functions as an output.
is the “definite integral of the function f(x) on the
interval [a, b].”
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Derivative
Basic Properties and Formulas
If f (x) and g (x) are differentiable functions (the derivative exists), c and n are any real numbers, then:
1.
2.
3.
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Derivative
4.
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6.
7.
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Derivative
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
DerivativeChain Rule Variants
The chain rule applied to some specific functions.
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Derivative
Examples :
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Derivative
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Derivative