Find the Derivative - d/d@VAR f(x)=2e^(3x-1)

Problem

d()/d(x)*2*e(3*x−1)

Solution

1. Identify the function as a constant multiple of an exponential function where the exponent is a linear function of x

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

2⋅d(e(3*x−1))/d(x)

3. Apply the chain rule for the exponential function eu where u=3*x−1

d(eu)/d(x)=eu⋅d(u)/d(x)

4. Differentiate the exponent 3*x−1 with respect to x

d(3*x−1)/d(x)=3

5. Multiply the results together to find the final derivative.

2⋅e(3*x−1)⋅3

6. Simplify the expression by multiplying the constants.

6*e(3*x−1)

Final Answer

(d(2)*e(3*x−1))/d(x)=6*e(3*x−1)

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