Find dy/dx y=(5x^2+11x)^20

Problem

d()/d(x)*(5*x2+11*x)20

Solution

1. Identify the outer function and the inner function to apply the Chain Rule.

2. Apply the Chain Rule by differentiating the outer power function while keeping the inner expression the same.

20*(5*x2+11*x)19

3. Differentiate the inner function 5*x2+11*x with respect to x

d(5*x2+11*x)/d(x)=10*x+11

4. Multiply the derivative of the outer function by the derivative of the inner function.

d(y)/d(x)=20*(5*x2+11*x)19*(10*x+11)

Final Answer

d(y)/d(x)=20*(10*x+11)*(5*x2+11*x)19

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