Matlab: Basic Differentiation and Integration with the syms symbolic variable

To perform basic calculus calculations with Matlab, declare symbolic variables with syms command:

>> syms x;
>> y = 3*x^3+2*x^2-4*x+5;

Hence y = 3x³+2x²-4x+5.

For differentiation, the derivative of y is y' = diff(y):

>> y_prime = diff(y)

y_prime =

9*x^2 + 4*x - 4

Hence y' = dy/dx = 9x²+4x-4.

For integration, the integral of y is ∫ y dy = int(y):

>> y_integral = int(y)

y_integral =

(3*x^4)/4 + (2*x^3)/3 - 2*x^2 + 5*x

Consequently, ∫ y dy = (3x⁴)/4 + (2x³)/3 - 2x² + 5x + c.

References

Glossary of calculus (Wikipedia)
微積分常用述語中英文對照 (交大微積分教學小組)
Basic Calculus Terms 基本微基分名詞 (Study EECC)
Matlab: Differentiation of sine and cosine functions