Find the Derivative - d/dx y=(4x^2+3)(3x-2)

Problem

d()/d(x)*(4*x2+3)*(3*x−2)

Solution

1. Identify the function as a product of two binomials, u=4*x2+3 and v=3*x−2

2. Apply the product rule, which states that d()/d(x)*u*v=ud(v)/d(x)+vd(u)/d(x)

3. Calculate the derivatives of the individual parts:

d(4*x2+3)/d(x)=8*x

d(3*x−2)/d(x)=3

4. Substitute these values into the product rule formula:

d(y)/d(x)=(4*x2+3)*(3)+(3*x−2)*(8*x)

5. Distribute the terms to expand the expression:

d(y)/d(x)=12*x2+9+24*x2−16*x

6. Combine like terms to find the final derivative:

d(y)/d(x)=36*x2−16*x+9

Final Answer

d()/d(x)*(4*x2+3)*(3*x−2)=36*x2−16*x+9

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