Find the Derivative - d/dx y=2x^3-4x

Problem

d()/d(x)*(2*x3−4*x)

Solution

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

d()/d(x)*(2*x3−4*x)=(d(2)*x3)/d(x)−(d(4)*x)/d(x)

2. Apply the power rule to the first term, 2*x3 The power rule states that (d(a)*xn)/d(x)=n⋅a*x(n−1)

(d(2)*x3)/d(x)=3⋅2*x(3−1)

(d(2)*x3)/d(x)=6*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)=1⋅4*x(1−1)

(d(4)*x)/d(x)=4

4. Combine the results of the individual derivatives to find the final expression.

d(y)/d(x)=6*x2−4

Final Answer

d()/d(x)*(2*x3−4*x)=6*x2−4

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