5.3.3 Using the Derivative Rules with Transcendental Functions Flashcards Preview

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Flashcards in 5.3.3 Using the Derivative Rules with Transcendental Functions Deck (8):
1

Using the Derivative Rules with Transcendental Functions

• Some functions are combinations of other functions, such as products or quotients. To differentiate these functions, it may be necessary to use several computational techniques, possibly more than once.
• Transcendental functions have unusual derivatives.

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note

- A transcendental function is a function that cannot be
expressed in terms of a variable raised to a power. You can use all of the different derivative rules when working with transcendental functions.
- To find the derivative of a composition of a composite function you will need to use the chain rule twice. Each
additional composite function within a function will require an additional chain rule.
- Notice that the exponent is the outside of this expression. Next is the sine function. The argument of the sine function is the final function.
- Here two functions are combined by multiplication. In addition, the second function is a composite function. To find the derivative you will need the product rule and the chain rule.
- Start with the product rule. Remember that you will need to use the chain rule when asked to find the derivative of the second piece of the product.
- This function is made up of the quotient of two other
functions. Notice that none of these functions are composite functions.
- Be careful when finding the derivative of the tangent
function. If you do not remember the formula you can derive it by converting tangent to sines and cosines.

3

Calculate the slope of the line tangent to f (x) = 1 + e^2x at x = 0.

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4

Find f′(x) if f(x)=cos(2x^2).

f′(x)=−4xsin(2x^2)

5

Suppose f(x)=2^(x^2−2x). Find f′(1).

f′(1)=0

6

Suppose f(x)=log_7x^2.What is the slope of the line tangent to f where x=2?

m=1/ln7

7

Use the definition of the derivative to evaluate the limit limh→0 ln(h+1)/h

lim h→0 ln(h+1)/h=1

8

Let f(x)=1−x^2+3x/2x^4. Rather than use the quotient rule to find f′(x), divide the denominator into the numerator first, and then find f′(x).

f′(x)=2x^2−9x−4/2x^5

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