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# Deriv calculus!

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### Deriv calculus!

1. 1. TheDERIVATIVERULES!
2. 2. The Table of Derivative Rules•What is a derivative?•Exponent Rule•Product Rule•Chain Rule•Trig. Rules•Natural Log•eˣ
3. 3. What’s a Derivative Derivative is the instant rate of change. There are several rules which make it easier to find the derivative. Today we will discover those rules!
4. 4. Express a Derivative? A derivative can be expressed by: • the lim as x → 0 of dy/dx • (f(x-Δx) – f(x))/ Δx • dy/dx
5. 5. The Rules
6. 6. Exponent Rule• The simplest ofthe derivativerules, applied to aletter such as x toa specific power.• xⁿ = nxn-1• Example: • x5 = 5x4
7. 7. Product rule applies when deriving two functions •This Rule which are multiplied. • f(x)g(x) is two functions multiplied • the derivative is: g(x)f’(x) + f(x)g’(x) •The process is as follows • make one function A and the other B; in this case A is f(x) and B is g(x) •Then derive each function separately • then multiply B*A’ and add it to A*B’
8. 8. Quotient Rule •This rule applies when deriving two functions which are being divided. • f(x)/g(x) is an example. •The derivative is (g(x)f’(x) – f(x)g’(x))/((g(x)2) • the process reach the derivative is as follows • make one function A and the other B; in this case A is f(x) and B is g(x) • derive each function separately • then multiply B*A’ and A*B’ • then B*A’ – A*B’ • then divide by B2
9. 9. Chain Rule One of the most important derivative rules, the chain rule applies when one function is within the other. For example : f(g(x)) To derive this, by using the chain rule, first derive the f function so in this case it would be f’g(x) Then derive the inside function in this case it would be g’(x) Then multiply the derivatives together making a final answer of f’g(x) *g’(x) Pay close attention to the inside equation as it may include other rules.
10. 10. Trig. Rules The easy stuff! Just memorize what the derivative of each function is and if needed apply the other rules. Function Derivative Sin(x) Cos(x) Cos(x) -Sin(x) Tan(x) Sec2(x) Cot(x) -CSC2(x) Sec(x) Sec(x)Tan(x) CSC(x) -CSC(x)Cot(x)
11. 11. New Rules (ln and ex) • ln(x) the derivative of this is 1/x • ex the derivative of this is ex These are mostly memorization as well, however you’ll be surprised that one of these functions derivatives is the same as the function.
12. 12. Now you’re ready… FOR THE QUIZ!