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

Problem

d()/d(x)*6*x*(3*x2−5*x)

Solution

1. Distribute the 6*x into the parentheses to simplify the expression before differentiating.

y=18*x3−30*x2

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

d(y)/d(x)=(d(18)*x3)/d(x)−(d(30)*x2)/d(x)

3. Calculate the derivative of the first term by multiplying the exponent by the coefficient and decreasing the exponent by one.

(d(18)*x3)/d(x)=54*x2

4. Calculate the derivative of the second term using the same power rule method.

(d(30)*x2)/d(x)=60*x

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

d(y)/d(x)=54*x2−60*x

Final Answer

d()/d(x)*6*x*(3*x2−5*x)=54*x2−60*x

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