Subjects
PRICING
COURSES
SIGN IN
Start Free Trial
Alex P.
Senior at University of the Pacific
Tutor Satisfaction Guarantee
Pre-Calculus
TutorMe
Question:

what is the derivative of x^3

Alex P.
Answer:

To find this, we must use the limit definition. Since the limit definition is stated as lim as x->0= (F(x+h)-F(x))/h we must use this formula. so f(x+h) = (x+h)^3. Multiplying this out would become x^3 +3x^2h+3xh^2 +h^3. Take this answer subtracting it with F(x) which is x^3 will give the equation. 3x^2h +3xh^2 and h^3. We know this is correct because every term is divisible by h. So when we divide (3x^2h+3xh^2+h^3)/h we are left with 3x^2 +3xh+ h^2. Lastly, since h is approaching zero, we assume that h is 0. Replacing all h with 0 gives 3x^2 + 3x(0) + (0)^2. Simplifying everything, the final answer is found to be 3x^2.

Calculus
TutorMe
Question:

Find the derivative of f(x) = sin(x^3) dx in respects to y.

Alex P.
Answer:

This is a simple use of U substitution. The first thing we need is to set u = x^3 as it is the easier function to derive. This gives the function f(x)= sin(u). Now we take the derivative of this function which gives the answer f(x)= cos(u). Next we must use the chain rule application which states that we derive the inside function also. so the derivative of the inside function will be 3x^2. now we are given f(x)=cos(u)*(3x^2), The last step we need to do is replace u with x^3 so the final answer will be F(x)= cos(x^3)*(3x^2)

Algebra
TutorMe
Question:

Given that a triangle's angle are 30, 60, 90, determine the hypotenuse of the triangle with sides 5 and 12

Alex P.
Answer:

This could be determined in two different ways. 1) We could use the Pythagorean Theorem which states A^2 + B^2 = C^2. Given that we have two sides, it is safe to assume that 5^2 + 12^2 = C^2. Since 5^2= 25 and 12^2 = 144, adding the two up will give 169. The square root of 169 is 13 so the missing length is 13. 2) We can use the property of SohCahToa. We are given two sides, so it is appropriate that we choose Soh or Cah (Sin = opposite/ hypotenuse/ Cos= adjacent/hypotenuse). A fun note to notice is that the larger the angle, the larger the number. Using this information, 30 degrees would correlate with the length 5 and 60 degrees would correlate with the length 12. Given this we can use sin(30)= 5/x. We can rewrite this as x= 5/sin(30). so the answer will be again 13.

Send a message explaining your
needs and Alex will reply soon.
Contact Alex
Ready now? Request a lesson.
Start Session
FAQs
What is a lesson?
A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
How do I begin a lesson?
If the tutor is currently online, you can click the "Start Session" button above. If they are offline, you can always send them a message to schedule a lesson.
Who are TutorMe tutors?
Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.