Join thousands of students who trust us to help them ace their exams!Watch the first video
Multiple Choice
What is the derivative of the function with respect to ?
A
B
C
D
Verified step by step guidance
1
Step 1: Recall the derivative rule for exponential functions. The derivative of e^{u} with respect to x is given by (d/dx)e^{u} = e^{u} * (du/dx), where u is a function of x.
Step 2: Identify the exponent in the given function f(x) = e^{3x}. Here, u = 3x.
Step 3: Compute the derivative of u = 3x with respect to x. Using basic differentiation rules, (du/dx) = 3.
Step 4: Apply the chain rule. Substitute u = 3x and (du/dx) = 3 into the formula for the derivative of e^{u}. This gives (d/dx)e^{3x} = e^{3x} * 3.
Step 5: Simplify the expression. The derivative of f(x) = e^{3x} with respect to x is f'(x) = 3e^{3x}.