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Calculus has always been a subject that students have trouble with. An understanding of calculus at the high school level is crucial to having success later in life at the highly competitive university level. Many students struggle with calculus because the subject is hard to apply to the real world sometimes. Calculus is a discipline in mathematics that focuses on limits, functions, integrals, derivatives and infinite series. Making sense of this and showing how this applies to the real world is something our San Diego Tutors have a lot of experience with. Most of our calculus tutors are math or physics majors with extensive calculus training. Below, you will find helpful calculus rules and equations to better guide you through your learning process. In addition, at the bottom of the page you will find some sample problems you can go over with you San Diego Tutor. San Diego Tutor has put together a great team of in home tutors in your area to help with calculus. CONTACT US today for more information on getting a calculus tutor in the Del Mar, La Jolla, Carmel Valley, Poway, Rancho Santa Fe and Scripps Ranch areas.
Helpful Calculus Formulas
Differentiation Formulas
- d/dx c = 0, c constant
- d/dx cf(x) = cf'(x), c constant
- d/dx [f(x) ± g(x)] = f'(x) ± g'(x)
- d/dx [f(x) * g(x)] = f(x) * g'(x) +
g(x) * f'(x) (product rule)
- d/dx [f(x) / g(x)] = (g(x)f'(x) -
f(x)g'(x))/([g(x)]2) (quotient rule)
Integration Formulas
Remember that u'dx = du and may be
replaced by du.
- ∫dx = x + c
- ∫k f(x) dx = k ∫f(x) dx
- ∫[f(x) ± g(x)]dx = ∫f(x)dx ± ∫g(x)dx
Sample Problems
Below you will find some sample calculus problems you may see on one of your exams. If you would like one of our San Diego Tutor educational specialists to go over the answers with you, please send your answers to practiceproblems@sandiegotutor.com and one of our representatives will contact you.
Integrate the following equations
1)∫xdx
2)∫x2dx
3)∫2x3dx
4)∫2x3 + 5x dx
Differentiate the following equation
1) f(x) = x3
2) f(x) = (x3 + 5x + 9)
3) f(x) = (x4 + 3x2 + 10x)
4) f(x) = ex + ex
Sir Isaac Newton was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is perceived and considered by a substantial number of scholars and the general public as one of the most influential men in history.
