Find the Derivative - d/dx 2e^xcos(x)

Problem

d()/d(x)*2*ex*cos(x)

Solution

1. Identify the constant and the functions involved. The expression is a product of the constant 2 the exponential function ex and the trigonometric function cos(x)

2. Apply the constant multiple rule to move the constant 2 outside of the derivative.

d()/d(x)*2*ex*cos(x)=2(d(ex)*cos(x))/d(x)

3. Apply the product rule, which states (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x) where u=ex and v=cos(x)

2(d(ex)*cos(x))/d(x)=2*(exd(cos(x))/d(x)+cos(x)d(ex)/d(x))

4. Differentiate the individual functions. The derivative of cos(x) is −sin(x) and the derivative of ex is ex

2*(ex*(−sin(x))+cos(x)*ex)

5. Simplify the expression by factoring out the common term ex and distributing the 2

2*ex*(cos(x)−sin(x))

Final Answer

(d(2)*ex*cos(x))/d(x)=2*ex*(cos(x)−sin(x))

Want more problems? Check here!