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

Problem

d()/d(x)*(x3−4*x)

Solution

1. Identify the expression to be differentiated, which is a polynomial consisting of two terms: x3 and −4*x

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

3. Apply the power rule to the first term, x3 The power rule d(xn)/d(x)=n*x(n−1) gives 3*x2

4. Apply the power rule to the second term, −4*x Since the exponent of x is 1, the derivative is −4*(1)*x0 which simplifies to −4

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

Final Answer

d(x3−4*x)/d(x)=3*x2−4

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