Get an answer in 5 minutes

Ask a question to our educators
MATHS

Prove, from first principles, that the derivative of 5xcubed is 15x squared. How would I do this?

The formula for derivatives from first principles is lim(h to 0) of [f(x+h)-f(x)]/h. So in this case f(x) is 5xcubed, and we want to show that when we use 5xcubed as f(x) in the formula and let h go to 0 we get 15xsquared. Since we're substituting 5xcubed as f(x), we know that 5(x+h)cubed is f(x+h). Expanding 5(x+h)cubed on the top of the fraction gives us: [5(xcubed + 3xsquared*h + 3x*hsquared + hcubed) - 5xcubed]/h. Once you multiply the 5 into the bracket, the 5xcubeds will cancel and then you can cancel an h from each remaining term on the top with the h underneath. This gives: 15xsquared + 15xh + 5hsquared Now as h goes to zero the first term doesn't change since it has no h but the second and third terms also go to zero. Leaving just 15xsquared.

Dan Kozlen
·

4.2k students helped

Maths

2x+6=7x-14

What is Q&A on Scoodle?

At Scoodle we understand that everyone learns in a different way. Some people learn through practice, using essays and notes; others prefer video lessons to watch and learn, some just need help with a specifically hard question, while some learn best 1-on-1 tutoring sessions. At Scoodle we cater for all types of learning styles and needs. From GCSE Maths video lessons to A-level English essays and specialist educators in every subject - we’ve got you covered.

Scoodle has helped over 131,000 students so far

Need help with Maths?

Getting expert help from a tutor is a great way to improve your Maths grades.

Discover learning resources by tutors

Learn Maths with Video Lessons
1hr 28m · 8 videos
Paja Kruzikova
·

706 students helped

GCSE Maths - Numbers
28m · 3 videos
Iqbal Lokman
·

1.6k students helped

1hr 32m · 9 videos
Paja Kruzikova
·

706 students helped

GCSE Maths - Ratios
56m · 6 videos
Paja Kruzikova
·

706 students helped

GCSE Maths - Algebra A
1hr 14m · 7 videos
Paja Kruzikova
·

706 students helped

GCSE Maths - Algebra B
1hr 27m · 9 videos
Paja Kruzikova
·

706 students helped

GCSE Maths - Algebra C