Find the Derivative - d/dx y=x-1/90x^3

Problem

d()/d(x)*(x−1/90*x3)

Solution

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

d()/d(x)*(x−1/90*x3)=d(x)/d(x)−d()/d(x)1/90*x3

2. Apply the power rule to the first term, where the derivative of x is 1

d(x)/d(x)=1

3. Apply the constant multiple rule and the power rule to the second term, multiplying the exponent by the coefficient and decreasing the exponent by 1

d()/d(x)1/90*x3=1/90⋅3*x2

4. Simplify the resulting fraction by dividing 3 and 90 by their greatest common divisor.

3/90*x2=1/30*x2

5. Combine the results to find the final derivative.

d(y)/d(x)=1−1/30*x2

Final Answer

d()/d(x)*(x−1/90*x3)=1−1/30*x2

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