What is the equation for the derivative of f\left(x\right)=g\left(x\right)h\left(x\right)?

f'(x) = g'\left(x\right)h\left(x\right)+g\left(x\right)h'\left(x\right)

What is the derivative of an equation of the form y=f\left(g\left(x\right)\right)?

y'=f'\left(g\left(x\right)\right)\cdot\left(g'\left(x\right)\right)

How do we find the critical points of a function?

Take first derivative, set equal to 0, and solve for zeros and undefined

How can you determine if a given function is increasing/decreasing? ** 'a' is a specific point you are testing*

f'\left(a\right) 0, f is increasing.

How do you feel about Jordan's shirt?

she's so funny and cool i want that shirt, this makes me love calculus

List all the derivative rules necessary to solve the derivative of \frac{\sin\left(7x\right)\left(4x^2\right)}{e^x}

Product rule, quotient rule , and chain rule

What is the derivative of an equation of the form e^{g\left(x\right)} ?

e^{g\left(x\right)}\cdot g'\left(x\right)

How do we find inflection points of a given function?

take the second derivative, set equal to 0, solve for zeros and undefined

What are the indeterminate forms that L'Hopital's Rule can be applied to?

\frac{0}{0} and \frac{∞}{∞}

What is the derivative of sec(x) ?

\sec\left(x\right)\tan\left(x\right)

What is the derivative of an equation of the form ln(g(x)) ?

\frac{1}{g\left(x\right)}\cdot\left(g'\left(x\right)\right), \frac{g'\left(x\right)}{g\left(x\right)}

When taking the derivative of a function with both x and y with respect to x...

multiply \frac{dy}{dx} after taking derivatives of terms with y in them

What is the derivative of an equation of the form f\left(x\right)=\frac{g\left(x\right)}{h\left(x\right)}?

f'(x) = (g'(x)h(x)-g(x)h'(x))/(h(x))2

studbud

Calc Review

20 termsStudBud Administration11 plays

Imported from external platform

Flashcards20 cardsFPractice quizPHost liveL

Questions 20

Answers

1
What is \lim_{x\to∞}\left(\frac{1}{x}\right) ?
Undefined
∞
0
1
2
What is the equation for the derivative of f\left(x\right)=g\left(x\right)h\left(x\right)?
f'\left(x\right)=g'\left(x\right)h'\left(x\right)
f'(x) = g'\left(x\right)h'\left(x\right)+h\left(x\right)g\left(x\right)
f'(x) = g'\left(x\right)h\left(x\right)+g\left(x\right)h'\left(x\right)
f'(x)= g'\left(x\right)h\left(x\right)-g\left(x\right)h'\left(x\right)
3
What is the derivative of an equation of the form y=f\left(g\left(x\right)\right)?
y'=f'\left(g'\left(x\right)\right)\cdot\left(g\left(x\right)\right)
y'=f'\left(g\left(x\right)\right)\cdot\left(g'\left(x\right)\right)
y'=f'\left(g'\left(x\right)\right)
y'=f\left(g'\left(x\right)\right)\cdot\left(f'\left(x\right)\right)
4
How do we find the critical points of a function?
Take the 12th derivative
Take first derivative, set equal to 0, and solve for zeros and undefined
Take second derivative, set it equal to 1, and solve for zeros.
Take first derivative, set it equal to 1, and solve.
5
How can you determine if a given function is increasing/decreasing? ** 'a' is a specific point you are testing*
f\left(a\right)>0, f is increasing. f\left(a\right)<0, f is decreasing.
f\left(a\right)=0, f is increasing. f\left(a\right)=1, f is decreasing.
f'\left(a\right)<0, f is decreasing. f'\left(a\right)>0, f is increasing.
f'\left(a\right)>0, f is decreasing. f'\left(a\right)<0, f is increasing.
6
How do you feel about Jordan's shirt?
she's so funny and cool i want that shirt
literally why is she wearing that its so weird
this makes me love calculus
i literally couldn't care less
7
List all the derivative rules necessary to solve the derivative of \frac{\sin\left(7x\right)\left(4x^2\right)}{e^x}
No rules needed! I can calculate this in my head :)
Product rule and chain rule
Product rule, quotient rule
Product rule, quotient rule , and chain rule
8
What is the derivative of an equation of the form e^{g\left(x\right)} ?
e^{g\left(x\right)}\cdot g'\left(x\right)
e^{g'\left(x\right)}
e^{g'\left(x\right)}\cdot g\left(x\right)
e^{g\left(x\right)}
9
How do we find inflection points of a given function?
take the first derivative, set equal to 0, and solve
take the second derivative, set equal to 0, solve for zeros and undefined
take the 3rd derivative
take the second derivative and divide by the first derivative
10
What are the indeterminate forms that L'Hopital's Rule can be applied to?
∞-∞ and ∞\cdot0
Only \frac{0}{0}
\frac{0}{0} and \frac{∞}{∞}
Only \frac{∞}{∞}
11
What is the derivative of sin(x)?
sin(2x)
-sin(x)
cos(x)sin(x)
cos(x)
12
What is \ \lim_{x\to0}\left(\frac{1}{x}\right) ?
∞
1
Undefined
0
13
What is the derivative of ln(x) ?
\frac{1}{x}
ln(2x)
We can't take the derivative of this.
\frac{1}{\log\left(x\right)}
14
What is the derivative of sec(x) ?
\sec\left(x\right)\tan\left(x\right)
\cos\left(x\right)\csc\left(x\right)
\tan^2\left(x\right)
\sec^2\left(x\right)
15
What is the derivative of an equation of the form ln(g(x)) ?
\frac{1}{g\left(x\right)}\cdot\left(g'\left(x\right)\right)
\frac{\ln\left(g\left(x\right)\right)}{g'\left(x\right)}
\frac{g'\left(x\right)}{\ln\left(x\right)}
\frac{g'\left(x\right)}{g\left(x\right)}
16
What is the derivative of tan(x) ?
sec(x)
tan2 (x)
sin(x)cos(x)
sec2(x)
17
What is the derivative of e^x ?
x^e
xe^x
e^x
Can't take the derivative.
18
When taking the derivative of a function with both x and y with respect to x...
nothing needs to be done, take normal derivatives.
multiply \frac{dy}{dx} after taking derivatives of terms with y in them
multiply \frac{dx}{dy} after taking derivatives of terms with x in them
multiply \frac{dx}{dy} after taking derivatives of terms with y in them
19
What is the derivative of an equation of the form f\left(x\right)=\frac{g\left(x\right)}{h\left(x\right)}?
f'(x) = (g'(x)h(x)+g(x)h'(x))/(h(x))2
f'(x) = (g'(x)h(x)+g(x)h'(x))/(h'(x))2
f'(x) = (g'(x)h(x)-g(x)h'(x))/(h(x))2
f'(x) = (g(x)h(x)-g'(x)h'(x))/(g(x))2
20
What is \int_{ }^{ }\cos\left(x\right)dx ?
-sin(x) + c
sec(x)
sin(x) + c
sin(x)

Calc Review Flashcards | StudBud