given the function f(x)=X^3 - 6X^2+9X. Find the first derivative of the function of f(x)

given the function f(x)=X^3 - 6X^2+9X. Find the first derivative of the function of f(x)

Answer 1

[Sam Chak]

You can use the first derivative formula from Larson/Edwards Calculus of a Single Variable textbook.

For more info, please look up for examples in this link:

https://www.mathworks.com/help/symbolic/differentiation.html

%% declare symbolic variable
syms x

%% function
a   = 3;
b   = 2;
c   = 1;
y   = x^a + 6*x^b - 9*x^c

y = 

%% 1st derivative formula
dy  = a*x^(a-1) + 6*b*x^(b-1) - 9*c*x^(c-1)

dy = 

fplot([y, dy], [-8, 4]), grid on, xlabel x, ylabel f(x)

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Answer 2

[Star Strider]

Use the polyder function —

f = @(x) x.^3 - 6*x.^2 + 9*x;                   % Anonymouus Function

p = [1 6 3 0]                                   % Coefficient Vector

p = 1×4

1 6 3 0

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dfdxp = polyder(p)                              % Polynomial Derivative

dfdxp = 1×3

3 12 3

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x = -10:0.1:10;

figure
plot(x, polyval(p,x), DisplayName='f(x)')
hold on
plot(x, polyval(dfdxp,x), DisplayName='f''(x)')
hold off
grid
legend(Location='best')

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You can also use the gradient funciton or the Symbolic Math Toolbox diff function for the derivative.

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