Find the Derivative - d/dx y=x^3-17x^2+63x+2

Problem

d()/d(x)*(x3−17*x2+63*x+2)

Solution

1. Apply the sum rule for differentiation, which allows for the derivative of each term to be taken individually.

d()/d(x)*(x3−17*x2+63*x+2)=d(x3)/d(x)−(d(17)*x2)/d(x)+(d(63)*x)/d(x)+d(2)/d(x)

2. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) to the terms x3 and x2

d(x3)/d(x)=3*x2

(d(17)*x2)/d(x)=17⋅2*x=34*x

3. Apply the linear rule to the term 63*x where the derivative of c*x is simply the constant c

(d(63)*x)/d(x)=63

4. Apply the constant rule to the term 2 noting that the derivative of any constant is 0

d(2)/d(x)=0

5. Combine the results to find the final derivative of the expression.

d(y)/d(x)=3*x2−34*x+63

Final Answer

d()/d(x)*(x3−17*x2+63*x+2)=3*x2−34*x+63

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