How do you find the derivative of # f(x) = 2e^x - 3x^4#?

Question

Emily Ammerman · Accepted Answer

#f^{'}(x)\ =\ 2e^x-12x^3#

# # # # The derivative of the given function is represented as: #d/dx(f(x))\ =\ d/dx(2e^x-3x^4)# # # Remember the sum/difference of derivative rule, which is applied when two function are being added/subtracted up. #(f\pm g)^'=f^'\pm g^'# # # #=\frac{d}{dx}(2e^x)-\frac{d}{dx}(3x^4)# Pull out the constant from the derivative. The rule is stated as: #(a\cdot f)^'=a\cdot f^'# #=2\frac{d}{dx}(e^x)-3\frac{d}{dx}(x^4)# # # Now at this point, we need to recall the power rule for derivative and exponential function rule. They are stated as: #\frac{d}{dx}(e^x)=e^x##" "#and#" "##\frac{d}{dx}(x^a)=a\cdot x^{a-1}# # # So that by applying these rules, we get: #=2e^x-3\cdot 4x^{4-1}# Simplify to get: #f^{'}(x)\ =\ 2e^x-12x^3# # # That's it!

Ezekiel Alexander · Answer

undefined To find the derivative of f(x) = 2e^x - 3x^4, you would differentiate each term separately using the rules of differentiation:

1. Differentiate the term 2e^x:
   The derivative of e^x is e^x, so the derivative of 2e^x is 2e^x.

2. Differentiate the term -3x^4:
   Apply the power rule, which states that the derivative of x^n is nx^(n-1). 
   So, the derivative of -3x^4 is -12x^3.

Therefore, the derivative of f(x) = 2e^x - 3x^4 is f'(x) = 2e^x - 12x^3.