3.9: Derivatives of Natural Logarithmic Functions

Miscellaneous

100

The ______ function of the natural logarithmic function f(x)=ln x is f^-1(x)=e^x

What is inverse?

200

What is the inverse of ln x?

What is e^x?

300

For all properties of exponents what must be true?

1. a&b are real numbers

2. m&n are integers

What is 1 and 2?

400

True or False? Every exponential function is a power of the natural exponential function. a^x=e^{ln x a}?

What is true?

500

Find dy/dx: y=4^{x^3+cosx}

Wht is y'+(ln 4)4^{x^3+cosx}(3x²-sinx)?

Properties of Exponents

100

a^m*aⁿ=a^m+n

what is product property?

200

(a^m)ⁿ=a^mn

What is power of a power property?

300

(ab)^m=a^mb^m

What is power of a product property?

400

a^-m=1/(a^m), a not = to 0

What is the negative exponent property?

500

a⁰=1: a not = 0

What is the zero exponent property?

Find y'

100

y=e^2x

what is y'=2e^2x?

200

y=e^-1/x

what is y'=(1/x²)e^-1/x?

300

y=sin(2x+e^x)

what is y'=cos(2x+e^x)(2+e^x)?

400

y=e^sinx

what is y'=e^sinxcosx?

500

y=(e^x)/(e^x+e^-x)

what is y'=2/(e^x+e^-x)²?

Characteristics of the graphs

100

What is the domain and range of the exponential function?

what is domain of all real numbers and a range of y>0?

200

Where are the x-intercepts on the parent function of an exponential function?

What is there are no x-intercepts?

300

True or False: The characteristics of the parent function of log is a range of all real numbers, a domain of x>0, there are no y-intercepts, an x-intercept at (1,0), an always increasing graph and a VA at x=0?

What is True?

400

Does a parent function of a log graph cross the x and y axis?

What is no?

500

True or False: The characteristics of the parent function of the exponential function is a domain of all real numbers, a range of y>0, there are no x-intercepts, a y-intercept at (1,0), an always decreasing graph and a HA at x=0?

What is false?