Find the Derivative - d/dx xe^(4x)

Problem

(d(x)*e(4*x))/d(x)

Solution

1. Identify the rule needed for the expression, which is a product of two functions, x and e(4*x)

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

3. Set u=x and v=e(4*x)

4. Find the derivatives of the individual parts: d(x)/d(x)=1 and d(e(4*x))/d(x)=4*e(4*x) using the chain rule.

5. Substitute these into the product rule formula: x*(4*e(4*x))+e(1)(4*x)

6. Simplify the expression by factoring out the common term e(4*x)

Final Answer

(d(x)*e(4*x))/d(x)=e(4*x)*(4*x+1)

Want more problems? Check here!