Find the Derivative - d/dx y=(2x^3+8)(3x^7-9)

Problem

d()/d(x)*(2*x3+8)*(3*x7−9)

Solution

1. Identify the rule needed for the derivative of a product of two functions, which is the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Assign the parts of the expression to u and v let u=2*x3+8 and v=3*x7−9

3. Differentiate each part individually using the power rule: d(u)/d(x)=6*x2 and d(v)/d(x)=21*x6

4. Substitute these components into the product rule formula:

(2*x3+8)*(21*x6)+(3*x7−9)*(6*x2)

5. Distribute the terms in the expression:

(42*x9+168*x6)+(18*x9−54*x2)

6. Combine like terms to simplify the final polynomial:

60*x9+168*x6−54*x2

Final Answer

d()/d(x)*(2*x3+8)*(3*x7−9)=60*x9+168*x6−54*x2

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