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How do you find the derivative of #f(x) = [3(x)^2] - 4x#?

Answer 1

Samantha Adkison

#f'(x)=6x-4#

We have:

#f(x)=3x^2-4x#

Remember the following rules:

The power rule: #d/dx[x^n]=nx^(n-1)# if #n# is a constant.

The constant multiplication rule:

If a variable is being multiplied by a constant, you can always bring the constant outside the derivative. For example:

#d/dx[3x]=3*d/dx[x]#

Subtraction rule (Here is an example):

#d/dx[x-2x]=d/dx[x]-d/dx[2x]#

Therefore:

#f'(x)=d/dx[3x^2-4x]#

#=>f'(x)=d/dx[3x^2]-d/dx[4x]#

#=>f'(x)=3*d/dx[x^2]-4*d/dx[x^1]#

#=>f'(x)=3*2*x^(2-1)-4*1*x^(1-1)#

#=>f'(x)=6*x^(1)-4*x^(0)#

#=>f'(x)=6*x-4*1#

#=>f'(x)=6x-4#

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Answer 2

Emma Aldridge

To find the derivative of ( f(x) = 3x^2 - 4x ), you can apply the power rule and the constant multiple rule of differentiation. The derivative of ( x^n ) with respect to ( x ) is ( nx^{n-1} ). The derivative of a constant multiple times a function is the constant multiple times the derivative of the function. Applying these rules, the derivative of ( f(x) ) is ( f'(x) = 6x - 4 ).

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Answer from HIX Tutor

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