Find the Derivative - d/dx y=3x(6x-5x^2)

Problem

d()/d(x)*3*x*(6*x−5*x2)

Solution

1. Distribute the term 3*x into the parentheses to simplify the expression before differentiating.

y=18*x2−15*x3

2. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) to each term individually.

d(y)/d(x)=(d(18)*x2)/d(x)−(d(15)*x3)/d(x)

3. Differentiate the first term by multiplying the exponent by the coefficient and decreasing the exponent by one.

(d(18)*x2)/d(x)=36*x

4. Differentiate the second term using the same power rule method.

(d(15)*x3)/d(x)=45*x2

5. Combine the results to find the final derivative.

d(y)/d(x)=36*x−45*x2

Final Answer

d()/d(x)*3*x*(6*x−5*x2)=36*x−45*x2

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