Find the Derivative - d/d@VAR f(x)=e^(1-20x+5x^2)

Problem

d()/d(x)*e(1−20*x+5*x2)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is eu and the inner function is u=1−20*x+5*x2

2. Apply the Chain Rule which states that d(eu)/d(x)=eu⋅d(u)/d(x)

3. Differentiate the inner function 1−20*x+5*x2 with respect to x using the Power Rule.

d(1−20*x+5*x2)/d(x)=−20+10*x

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

d(e(1−20*x+5*x2))/d(x)=e(1−20*x+5*x2)⋅(−20+10*x)

5. Rearrange the expression to place the polynomial factor in front of the exponential term.

d(e(1−20*x+5*x2))/d(x)=(10*x−20)*e(1−20*x+5*x2)

Final Answer

d(e(1−20*x+5*x2))/d(x)=(10*x−20)*e(1−20*x+5*x2)

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