Matlab: Differentiation of sine and cosine functions

To calculate the derivates of sin() and cos(), use the syms symbolic variable as below:

>> syms x
>> y = sin(x);
>> y_prime = diff(y)

y_prime =

cos(x)

>> y_prime_prime = diff(y_prime)

y_prime_prime =

-sin(x)

References

Matlab: Basic Differentiation and Integration with the syms symbolic variable
Basic Calculus Terms 基本微基分名詞

Basic Calculus Terms 基本微基分名詞

calculus 微積分

differentiation 微分
integration 積分

derivative 導數
integral 積分

References

Glossary of calculus (Wikipedia)
微積分常用述語中英文對照
Matlab: Basic Differentiation and Integration with the syms symbolic variable
Matlab: Differentiation of sine and cosine functions

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