Find the Derivative - d/dx f(x)=xe^(-x^2)

Problem

d()/d(x)*x*e(−x2)

Solution

1. Identify the rule needed for the expression, which is the product rule for u⋅v where u=x and v=e(−x2)

2. Apply the product rule formula d()/d(x)*u*v=ud(v)/d(x)+vd(u)/d(x)

3. Differentiate the first part u=x to get d(x)/d(x)=1

4. Differentiate the second part v=e(−x2) using the chain rule, which gives d(e(−x2))/d(x)=e(−x2)⋅(−2*x)

5. Substitute these derivatives back into the product rule formula.

x*(e(−x2)⋅−2*x)+e(1)(−x2)

6. Simplify the expression by multiplying the terms and factoring out the common term e(−x2)

−2*x2*e(−x2)+e(−x2)

e(−x2)*(1−2*x2)

Final Answer

(d(x)*e(−x2))/d(x)=e(−x2)*(1−2*x2)

Want more problems? Check here!