Find the Derivative - d/dx 3e^(-x^3)

Problem

(d(3)*e(−x3))/d(x)

Solution

1. Identify the constant multiple rule, which allows the constant 3 to be moved outside the derivative.

(d(3)*e(−x3))/d(x)=3d(e(−x3))/d(x)

2. Apply the chain rule for the exponential function, where d(eu)/d(x)=eud(u)/d(x) with u=−x3

3d(e(−x3))/d(x)=3*e(−x3)(d(−)*x3)/d(x)

3. Differentiate the exponent −x3 using the power rule.

(d(−)*x3)/d(x)=−3*x2

4. Substitute the derivative of the exponent back into the expression.

3*e(−x3)*(−3*x2)

5. Simplify the expression by multiplying the constants 3 and −3

−9*x2*e(−x3)

Final Answer

(d(3)*e(−x3))/d(x)=−9*x2*e(−x3)

Want more problems? Check here!