my calculus 1 differentiation quiz

This is the second quiz I gave to my calculus 1 students this semester. This quiz has 10 questions ALL on derivatives. Be sure you know the derivatives of power functions, derivatives of trigonometric functions, derivatives of inverse trigonometric functions, derivatives of exponential functions, derivatives of logarithmic functions. Of course, we also need to know all the derivative rules: the power rule, the product rule, the quotient rule, the chain rule, implicit differentiation, and logarithmic differentiation.

0:00 dy/dx for y=(sin(x))^x
3:00 derivative of e^tan^-1(x^2)
4:15 derivative of x/(1+ln(x))
5:30 d^2y/dx^2 for 9x^2+y^2=9
10:32 second derivative of e^(-x^2)
12:20 dy/dx for sqrt(x)+sqrt(y)=1
13:55 derivative of cos(x)*tan(x)
14:44 derivative of sec(x^3)
15:34 derivative of sqrt(x)/(1+x^2)
18:00 derivative of ln(x^2/(x^3+4))

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#justcalculus

[literallydeadpool]

I have to thank you so much for giving people who aren’t even in your class free calculus problems and answers!!! You’re among the most honorable of teachers!!!

[Andy-jubb]

It's interesting how when I went through school in the mid to late 1990s, it was drummed into us that you always put any positive values first. So with the last question, we would have been expected to write the numerator as 8-X^3, and not -X^3+8, to receive full marks.
I don't know if that is just a British or European thing to have the positive values at the start, or if it was an old preference that people have just stopped using.

[PrivatePug]

10:02 I was surprised when you used the fact that the original equation was equal to 9 again. It shows how attention to detail really helps you.

[kingbeauregard]

I guess we can think of the power rule as just a special case of taking the natural log and doing implicit differentiation. if y = x^n, then lny = n*lnx, (1/y)*dy/dx = n/x, and dy/dx = n*x^(n-1). There is something to be said for adopting a strategy of, any time you see exponentiation, just take the ln of both sides and see what happens; that way you can't make the mistake of mis-diagnosing which formula applies.

[Stephen_]

I like your e painting or something like that in your wall

[petereziagor]

I think I'll get 10 here
At least 90% of all the calculus I know is from your channel, thank you

[AlfonsoNeilJimenezCasallas]

teacher, I solved the first exercise using the same approach you proposed for derivative of x^x and I got the same result, great!

[petereziagor]

I think I have seen that number 4 somewhere in your channel 😺

[AnakinSkywalker-zqlm]

You just give them ten questions? Where does he teach? And when can I apply?

[DARKi]

Some of this questions are funny
Because somebody could not apply the properties, and complicate the work
Did you ever managed to find this type of students?

[yuudachiq]

studying for UNGEE, but tired. clicked this video, i'd like to follow and practice. of course, i'm learning english too.

[LaurentAbiteboul]

Hello !
Thank you for all your videos.
I’m wondering why don’t you try to go further and find dy/dx with only x parameters ?
For example, in Q6: because sqrt(y)=1-sqrt(x)
Can’t we simplify : dy/dx=(sqrt(x)-1)/sqrt(x)
Or dy/dx=1-1/sqrt(x)
?
Thank you

[matteocilla]

i just have one question over the derivative of (f/g)’, why we didn’t develop the dénominator ?(g^2)

[manjoker]

please solve this
integral ( log(x lnx) )/x dx