Find the Derivative - d/dx y=5x^3-4x^2+3x-6

Problem

d()/d(x)*(5*x3−4*x2+3*x−6)

Solution

1. Apply the sum rule for derivatives, which allows for the differentiation of each term in the polynomial individually.

d()/d(x)*(5*x3−4*x2+3*x−6)=(d(5)*x3)/d(x)−(d(4)*x2)/d(x)+(d(3)*x)/d(x)−d(6)/d(x)

2. Apply the power rule (d(a)*xn)/d(x)=a*n*x(n−1) to the first three terms of the expression.

(d(5)*x3)/d(x)=15*x2

(d(4)*x2)/d(x)=8*x

(d(3)*x)/d(x)=3

3. Apply the constant rule to the final term, noting that the derivative of any constant is zero.

d(6)/d(x)=0

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

d(y)/d(x)=15*x2−8*x+3

Final Answer

d()/d(x)*(5*x3−4*x2+3*x−6)=15*x2−8*x+3

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