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

Problem

d()/d(x)*(5*x2+2)*(3*x−2)

Solution

1. Identify the product rule formula, which states that for a function y=u⋅v the derivative is d(y)/d(x)=u⋅d(v)/d(x)+v⋅d(u)/d(x)

2. Assign the parts of the expression to u and v such that u=5*x2+2 and v=3*x−2

3. Differentiate each part individually to find d(u)/d(x)=10*x and d(v)/d(x)=3

4. Substitute these components into the product rule formula.

d(y)/d(x)=(5*x2+2)*(3)+(3*x−2)*(10*x)

5. Distribute the terms to expand the expression.

d(y)/d(x)=15*x2+6+30*x2−20*x

6. Combine like terms to reach the final simplified derivative.

d(y)/d(x)=45*x2−20*x+6

Final Answer

d()/d(x)*(5*x2+2)*(3*x−2)=45*x2−20*x+6

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