Find the Derivative - d/dx e^(1-20x+5x^2)

Problem

d(e^(1−20*x+5*x^2))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is e^u and the inner function is u=1−20*x+5*x^2

2. Apply the Chain Rule which states that the derivative of e^u(x) is e^u(x)⋅d(u)/d(x)

3. Differentiate the inner function 1−20*x+5*x^2 with respect to x using the Power Rule.

d(1−20*x+5*x^2)/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*x^2))/d(x)=e^(1−20*x+5*x^2)⋅(−20+10*x)

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

d(e^(1−20*x+5*x^2))/d(x)=(10*x−20)*e^(1−20*x+5*x^2)

Final Answer

d(e^(1−20*x+5*x^2))/d(x)=(10*x−20)*e^(1−20*x+5*x^2)

Want more problems? Check here!