Find the Derivative - d/dx y=10x^3+9x^2

Problem

d()/d(x)*(10*x3+9*x2)

Solution

1. Identify the rule needed for differentiation, which is the power rule: d(xn)/d(x)=n*x(n−1)

2. Apply the power rule to the first term, 10*x3 by multiplying the coefficient by the exponent and decreasing the exponent by one.

3. Differentiate the first term:

(d(10)*x3)/d(x)=30*x2

4. Apply the power rule to the second term, 9*x2 using the same process.

5. Differentiate the second term:

(d(9)*x2)/d(x)=18*x

6. Combine the results using the sum rule for derivatives.

Final Answer

d()/d(x)*(10*x3+9*x2)=30*x2+18*x

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