Find the Derivative - d/dx y=5x^3-4x

Problem

d()/d(x)*(5*x3−4*x)

Solution

1. Identify the expression as a polynomial and apply the sum/difference rule for derivatives, which allows for differentiating each term independently.

2. Apply the power rule to the first term, 5*x3 Multiply the coefficient by the exponent and decrease the exponent by one.

(d(5)*x3)/d(x)=5⋅3*x(3−1)=15*x2

3. Apply the power rule to the second term, −4*x Since the exponent of x is 1, the derivative is simply the coefficient.

(d(4)*x)/d(x)=4⋅1*x(1−1)=4

4. Combine the results to find the final derivative of the function.

Final Answer

d()/d(x)*(5*x3−4*x)=15*x2−4

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